Independent Submission                                         T. Pornin
Request for Comments: 6979                                   August 2013
Category: Informational
ISSN: 2070-1721

Deterministic Usage of the Digital Signature Algorithm (DSA) and Elliptic Curve Digital Signature Algorithm (ECDSA)




This document defines a deterministic digital signature generation procedure. Such signatures are compatible with standard Digital Signature Algorithm (DSA) and Elliptic Curve Digital Signature Algorithm (ECDSA) digital signatures and can be processed with unmodified verifiers, which need not be aware of the procedure described therein. Deterministic signatures retain the cryptographic security features associated with digital signatures but can be more easily implemented in various environments, since they do not need access to a source of high-quality randomness.


Status of This Memo


This document is not an Internet Standards Track specification; it is published for informational purposes.

このドキュメントはInternet Standards Trackの仕様ではありません。情報提供を目的として公開されています。

This is a contribution to the RFC Series, independently of any other RFC stream. The RFC Editor has chosen to publish this document at its discretion and makes no statement about its value for implementation or deployment. Documents approved for publication by the RFC Editor are not a candidate for any level of Internet Standard; see Section 2 of RFC 5741.

これは、他のRFCストリームとは無関係に、RFCシリーズへの貢献です。 RFCエディターは、このドキュメントを独自の裁量で公開することを選択し、実装または展開に対するその価値については何も述べていません。 RFC Editorによって公開が承認されたドキュメントは、どのレベルのインターネット標準の候補にもなりません。 RFC 5741のセクション2をご覧ください。

Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at


Copyright Notice


Copyright (c) 2013 IETF Trust and the persons identified as the document authors. All rights reserved.

Copyright(c)2013 IETF Trustおよびドキュメントの作成者として識別された人物。全著作権所有。

This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents ( in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document.

この文書は、BCP 78およびこの文書の発行日に有効なIETF文書に関するIETFトラストの法的規定(の対象となります。これらのドキュメントは、このドキュメントに関するあなたの権利と制限を説明しているため、注意深く確認してください。

Table of Contents


   1. Introduction ....................................................3
      1.1. Requirements Language ......................................4
   2. DSA and ECDSA Notations .........................................4
      2.1. Key Parameters .............................................5
      2.2. Key Pairs ..................................................5
      2.3. Integer Conversions ........................................6
           2.3.1. Bits and Octets .....................................6
           2.3.2. Bit String to Integer ...............................6
           2.3.3. Integer to Octet String .............................7
           2.3.4. Bit String to Octet String ..........................7
           2.3.5. Usage ...............................................8
      2.4. Signature Generation .......................................8
   3. Deterministic DSA and ECDSA ....................................10
      3.1. Building Blocks ...........................................10
           3.1.1. HMAC ...............................................10
      3.2. Generation of k ...........................................10
      3.3. Alternate Description of the Generation of k ..............12
      3.4. Usage Notes ...............................................13
      3.5. Rationale .................................................13
      3.6. Variants ..................................................14
   4. Security Considerations ........................................15
   5. Intellectual Property Status ...................................17
   6. References .....................................................17
      6.1. Normative References ......................................17
      6.2. Informative References ....................................18
   Appendix A.  Examples .............................................20
     A.1.  Detailed Example ..........................................20
       A.1.1.  Key Pair ..............................................20
       A.1.2.  Generation of k .......................................20
       A.1.3.  Signature .............................................23
     A.2.  Test Vectors ..............................................24
       A.2.1.  DSA, 1024 Bits ........................................25
       A.2.2.  DSA, 2048 Bits ........................................27
       A.2.3.  ECDSA, 192 Bits (Prime Field) .........................29
       A.2.4.  ECDSA, 224 Bits (Prime Field) .........................31
       A.2.5.  ECDSA, 256 Bits (Prime Field) .........................33
       A.2.6.  ECDSA, 384 Bits (Prime Field) .........................35
       A.2.7.  ECDSA, 521 Bits (Prime Field) .........................38
       A.2.8.  ECDSA, 163 Bits (Binary Field, Koblitz Curve) .........42
       A.2.9.  ECDSA, 233 Bits (Binary Field, Koblitz Curve) .........44
       A.2.10. ECDSA, 283 Bits (Binary Field, Koblitz Curve) .........46
       A.2.11. ECDSA, 409 Bits (Binary Field, Koblitz Curve) .........49
       A.2.12. ECDSA, 571 Bits (Binary Field, Koblitz Curve) .........52
       A.2.13. ECDSA, 163 Bits (Binary Field, Pseudorandom Curve) ....56
       A.2.14. ECDSA, 233 Bits (Binary Field, Pseudorandom Curve) ....58
       A.2.15. ECDSA, 283 Bits (Binary Field, Pseudorandom Curve) ....60
       A.2.16. ECDSA, 409 Bits (Binary Field, Pseudorandom Curve) ....63
       A.2.17. ECDSA, 571 Bits (Binary Field, Pseudorandom Curve) ....66
     A.3.  Sample Code ...............................................70
1. Introduction
1. はじめに

DSA [FIPS-186-4] and ECDSA [X9.62] are two standard digital signature schemes. They provide data integrity and verifiable authenticity in various protocols.

DSA [FIPS-186-4]とECDSA [X9.62]は、2つの標準デジタル署名方式です。これらは、さまざまなプロトコルでデータの整合性と検証可能な信頼性を提供します。

One characteristic of DSA and ECDSA is that they need to produce, for each signature generation, a fresh random value (hereafter designated as k). For effective security, k must be chosen randomly and uniformly from a set of modular integers, using a cryptographically secure process. Even slight biases in that process may be turned into attacks on the signature schemes.


The need for a cryptographically secure source of randomness proves to be a hindrance to deployment of DSA and ECDSA signature schemes in some architectures in which secure random number generation is challenging, in particular, embedded systems such as smartcards. In those systems, the RSA signature algorithm, used as specified in Public-Key Cryptography Standards (PKCS) #1 [RFC3447] (with "type 1" padding, not the Probabilistic Signature Scheme (PSS)) and ISO 9796-2 [ISO-9796-2], is often preferred, even though it is computationally more expensive, because RSA (with such padding schemes) is deterministic and thus does not require a source of randomness.

暗号化された安全な乱数の発生源の必要性は、安全な乱数の生成が困難な一部のアーキテクチャ、特にスマートカードなどの組み込みシステムにおいて、DSAおよびECDSA署名方式の展開を妨げることを証明しています。これらのシステムでは、RSA署名アルゴリズムは、公開鍵暗号化標準(PKCS)#1 [RFC3447](「タイプ1」のパディングで、確率的署名方式(PSS)ではありません)およびISO 9796-2 [ISO RSA(このようなパディング方式を使用)は決定論的であり、ランダム性のソースを必要としないため、計算コストは​​高くなりますが、-9796-2]がよく使用されます。

The randomized nature of DSA and ECDSA also makes implementations harder to test. Automatic tests cannot reliably detect whether the implementation uses a source of randomness of high enough quality. This makes the implementation process more vulnerable to catastrophic failures, often discovered after the system has been deployed and successfully attacked.


It is possible to turn DSA and ECDSA into deterministic schemes by using a deterministic process for generating the "random" value k. That process must fulfill some cryptographic characteristics in order to maintain the properties of verifiability and unforgeability expected from signature schemes; namely, for whoever does not know the signature private key, the mapping from input messages to the corresponding k values must be computationally indistinguishable from what a randomly and uniformly chosen function (from the set of messages to the set of possible k values) would return.


This document describes such a procedure. It has the following features:


o Produced signatures remain fully compatible with plain DSA and ECDSA. Entities that verify the signatures need not be changed or even be aware of the process used to generate k.

o 作成された署名は、プレーンDSAおよびECDSAとの完全な互換性を維持しています。署名を検証するエンティティは変更する必要がなく、kを生成するために使用されるプロセスを認識する必要さえありません。

o Key pair generation is not altered. Existing private keys can be used with deterministic DSA and ECDSA.

o 鍵ペアの生成は変更されません。既存の秘密鍵は、確定的DSAおよびECDSAで使用できます。

o Using deterministic DSA and ECDSA implies no extra storage requirement of any secret or public value.

o 確定的DSAおよびECDSAの使用は、秘密または公開の値の追加のストレージ要件を意味しません。

o Deterministic DSA and ECDSA can be applied over the same inputs as plain DSA and ECDSA, namely a hash value computed over the message that is to be signed, with a cryptographically secure hash function.

o 確定的DSAおよびECDSAは、プレーンDSAおよびECDSAと同じ入力、つまり、暗号化された安全なハッシュ関数を使用して、署名されるメッセージに対して計算されたハッシュ値に適用できます。

Some relatively arbitrary choices were taken in the definition of deterministic (EC)DSA as specified in this document; this was done in order to make it as universally applicable as possible, so as to maximize usefulness of included test vectors. See Section 3.6 for a discussion of some possible variants.


It shall be noted that key pair generation still requires a source of randomness. In embedded systems where quality of randomness is an issue, it can often be arranged that key pair generation occurs within more controlled conditions (e.g., during a special smartcard initialization procedure or under physical control of sworn agents) or the key might even be generated elsewhere and imported in the device. Deterministic DSA and ECDSA only deal with the need for randomness at the time of signature generation.


1.1. Requirements Language
1.1. 要件言語

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC 2119 [RFC2119].

このドキュメントのキーワード「MUST」、「MUST NOT」、「REQUIRED」、「SHALL」、「SHALL NOT」、「SHOULD」、「SHOULD NOT」、「RECOMMENDED」、「MAY」、および「OPTIONAL」は、 RFC 2119 [RFC2119]で説明されているように解釈されます。

2. DSA and ECDSA Notations
2. DSAおよびECDSA表記

In this section, we succinctly describe DSA and ECDSA and define our notations. The complete specifications for DSA and ECDSA can be found in [FIPS-186-4] and [X9.62], respectively.

このセクションでは、DSAとECDSAを簡潔に説明し、表記法を定義します。 DSAとECDSAの完全な仕様は、それぞれ[FIPS-186-4]と[X9.62]にあります。

2.1. Key Parameters
2.1. 主なパラメータ

DSA and ECDSA work over a large group of prime size, in which the group operation is easy to compute, but the discrete logarithm is computationally infeasible with existing and foreseeable technology. The definition of the group is called the "key parameters". Key parameters may be shared between different key pairs with no ill effect on security; this is the usual case with ECDSA in particular.


DSA uses the following key parameters:


p a large prime number (at least 1024 bits)


q a sufficiently large prime number (at least 160 bits) that is also a divisor of p-1

q p-1の約数でもある十分に大きな素数(少なくとも160ビット)

g a generator for the multiplicative subgroup of order q of integers modulo p

g pを法とする整数の次数qの乗法サブグループのジェネレータ

The group on which DSA will be computed consists of the values 'g^j mod p', where '^' denotes exponentiation and j ranges from 0 to q-1 (inclusive). The size of the group is q.

DSAが計算されるグループは、値 'g ^ j mod p'で構成されます。ここで、 '^'は指数を示し、jの範囲は0〜q-1(両端を含む)です。グループのサイズはqです。

ECDSA uses the following key parameters:


E an elliptic curve, defined over a given finite field


q a sufficiently large prime number (at least 160 bits) that is a divisor of the curve order


G a point of E, of order q


The group on which ECDSA will be computed consists of the curve points jG (multiplication of point G by integer j) where j ranges from 0 to q-1. G is such that qG = 0 (the "point at infinity" on the curve E). The size of the group is q. Note that these notations slightly differ from those described in [X9.62]; we use them in order to match those used for DSA.

ECDSAが計算されるグループは、カーブポイントjG(ポイントGの整数jによる乗算)で構成されます。jの範囲は0〜q-1です。 GはqG = 0(曲線Eの「無限遠点」)です。グループのサイズはqです。これらの表記法は、[X9.62]で説明されている表記法とは少し異なることに注意してください。 DSAに使用されるものと一致させるために使用します。

2.2. Key Pairs
2.2. キーペア

A DSA or ECDSA private key is an integer x taken modulo q. The relevant standards prescribe that x shall not be 0; hence, x is an integer in the range [1, q-1].


A DSA or ECDSA public key is computed from the private key x and the key parameters:


o For DSA, the public key is the integer: y = g^x mod p

o DSAの場合、公開鍵は整数です:y = g ^ x mod p

o For ECDSA, the public key is the curve point: U = xG

o ECDSAの場合、公開鍵はカーブポイントです:U = xG

2.3. Integer Conversions
2.3. 整数変換

Let qlen be the binary length of q. qlen is the smallest integer such that q is less than 2^qlen. This is the size of the binary representation of q without a sign bit (note that q, being a big prime, is odd, thus avoiding any ambiguity about the length of any integer equal to a power of 2). We define five conversion functions, which work on strings of bits, octets, and integers modulo q. qlen is the main parameter for these conversions.

qlenをqのバイナリ長とする。 qlenは、qが2 ^ qlenより小さいような最小の整数です。これは、符号ビットなしのqのバイナリ表現のサイズです(大きな素数であるqは奇数なので、2のべき乗に等しい整数の長さについてのあいまいさを回避します)。ビット、オクテット、およびqを法とする整数のストリングで機能する5つの変換関数を定義します。 qlenは、これらの変換の主要なパラメーターです。

In the following subsections, we use two other lengths, called blen and rlen. rlen is equal to qlen, rounded up to the next multiple of 8 (if qlen is already a multiple of 8, then rlen equals qlen; otherwise, rlen is slightly larger, up to qlen+7). Note that rlen is unrelated to the value r, the first half of a generated signature. blen is the length (in bits) of an input sequence of bits and may vary between calls. blen may be smaller than, equal to, or larger than qlen.

以下のサブセクションでは、blenとrlenと呼ばれる他の2つの長さを使用します。 rlenはqlenに等しく、次の8の倍数に切り上げられます(qlenがすでに8の倍数である場合、rlenはqlenに等しくなります。それ以外の場合、rlenはわずかに大きく、qlen + 7まで)。 rlenは、生成された署名の前半である値rとは関係がないことに注意してください。 blenは、ビットの入力シーケンスの長さ(ビット単位)であり、呼び出し間で異なる場合があります。 blenは、qlenよりも小さい、等しい、または大きい場合があります。

2.3.1. Bits and Octets
2.3.1. ビットとオクテット

Formally, all operations are defined on sequences of bits. A sequence is ordered; the first bit is said to be leftmost, while the last bit is rightmost.


On most software systems, bits are grouped into octets (sequences of eight bits). Binary data, e.g., the output of a hash function, is available as a sequence of octets. Whenever applicable, we consider that bits within an octet are ordered from most significant to least significant: the first (leftmost) bit within an octet has numerical value 128, while the last (rightmost) has numerical value 1.


2.3.2. Bit String to Integer
2.3.2. 整数へのビット文字列

The bits2int transform takes as input a sequence of blen bits and outputs a non-negative integer that is less than 2^qlen. It consists of the following steps: 1. The sequence is first truncated or expanded to length qlen:

bits2int変換は、入力としてblenビットのシーケンスを取り、2 ^ qlen未満の非負の整数を出力します。これは次の手順で構成されます。1.シーケンスは最初に切り捨てられるか、長さqlenに拡張されます。

* if qlen < blen, then the qlen leftmost bits are kept, and subsequent bits are discarded;

* qlen <blenの場合、qlenの左端のビットが保持され、後続のビットは破棄されます。

* otherwise, qlen-blen bits (of value zero) are added to the left of the sequence (i.e., before the input bits in the sequence order).

* それ以外の場合は、qlen-blenビット(値がゼロ)がシーケンスの左側に追加されます(つまり、シーケンス順の入力ビットの前)。

2. The resulting sequence is then converted to an integer value using the big-endian convention: if input bits are called b_0 (leftmost) to b_(qlen-1) (rightmost), then the resulting value is:

2. 結果のシーケンスは、ビッグエンディアン規則を使用して整数値に変換されます。入力ビットがb_0(左端)からb_(qlen-1)(右端)と呼ばれる場合、結果の値は次のようになります。

          b_0*2^(qlen-1) + b_1*2^(qlen-2) + ... + b_(qlen-1)*2^0

The bits2int transform can also be described in the following way: the input bit sequence (of length blen) is transformed into an integer using the big-endian convention. Then, if blen is greater than qlen, the resulting integer is divided by two to the power blen-qlen (Euclidian division: the remainder is discarded); in many software implementations of arithmetics on big integers, that division is equivalent to a "right shift" by blen-qlen bits.


2.3.3. Integer to Octet String
2.3.3. 整数からオクテット文字列へ

An integer value x less than q (and, in particular, a value that has been taken modulo q) can be converted into a sequence of rlen bits, where rlen = 8*ceil(qlen/8). This is the sequence of bits obtained by big-endian encoding. In other words, the sequence bits x_i (for i ranging from 0 to rlen-1) are such that:

qより小さい整数値x(および、特に、qを法として取られた値)は、rlenビットのシーケンスに変換できます。ここで、rlen = 8 * ceil(qlen / 8)です。これは、ビッグエンディアンエンコーディングによって取得されたビットのシーケンスです。つまり、シーケンスビットx_i(iの範囲は0からrlen-1まで)は次のようになります。

      x = x_0*2^(rlen-1) + x_1*2^(rlen-2) + ... + x_(rlen-1)

We call this transform int2octets. Since rlen is a multiple of 8 (the smallest multiple of 8 that is not smaller than qlen), then the resulting sequence of bits is also a sequence of octets, hence the name.

この変換をint2octetsと呼びます。 rlenは8の倍数(qlen以上の最小の8の倍数)であるため、結果として得られるビットのシーケンスもオクテットのシーケンス、つまり名前になります。

2.3.4. Bit String to Octet String
2.3.4. ビット文字列からオクテット文字列

The bits2octets transform takes as input a sequence of blen bits and outputs a sequence of rlen bits. It consists of the following steps:


1. The input sequence b is converted into an integer value z1 through the bits2int transform:

1. 入力シーケンスbは、bits2int変換によって整数値z1に変換されます。

z1 = bits2int(b)

z1 = bits2int(b)

2. z1 is reduced modulo q, yielding z2 (an integer between 0 and q-1, inclusive):

2. z1はqを法として縮小され、z2(0からq-1までの整数)を生成します。

          z2 = z1 mod q

Note that since z1 is less than 2^qlen, that modular reduction can be implemented with a simple conditional subtraction: z2 = z1-q if that value is non-negative; otherwise, z2 = z1.

z1は2 ^ qlen未満であるため、そのモジュラー削減は単純な条件付き減算で実装できることに注意してください。z2= z1-qその値が負でない場合。それ以外の場合、z2 = z1。

3. z2 is transformed into a sequence of octets (a sequence of rlen bits) by applying int2octets.

3. z2は、int2octetsを適用することにより、オクテットのシーケンス(rlenビットのシーケンス)に変換されます。

2.3.5. Usage
2.3.5. 使用法

It is worth noting that int2octets is not the reverse of bits2int, even for input sequences of length qlen: int2octets will add some bits on the left, while bits2int will discard some bits on the right. int2octets is the reverse of bits2int only when qlen is a multiple of 8 and bit sequences already have length qlen.

長さqlenの入力シーケンスであっても、int2octetsはbits2intの逆ではないことに注意してください。int2octetsは左側にいくつかのビットを追加し、bits2intは右側にいくつかのビットを破棄します。 int2octetsは、qlenが8の倍数であり、ビットシーケンスの長さがすでにqlenである場合にのみ、bits2intの逆になります。

bits2int is used during signature generation and verification in standard DSA and ECDSA to transform a hash value (computed over the input message) into an integer modulo q. That is, the integer obtained through bits2int is further reduced modulo q; since that integer is less than 2^qlen, that reduction can be performed with at most one subtraction.

bits2intは、標準DSAおよびECDSAでの署名の生成および検証中に使用され、ハッシュ値(入力メッセージで計算された)をqを法とした整数に変換します。つまり、bits2intを介して取得された整数は、qを法としてさらに縮小されます。その整数は2 ^ qlenより小さいため、その削減は最大で1つの減算で実行できます。

int2octets is defined under the name "Integer-to-OctetString" in Section 2.3.7 of SEC 1 [SEC1]. It is used in the specification of the encoding of an ECDSA private key (x) within an ASN.1-based structure.

int2octetsは、SEC 1 [SEC1]のセクション2.3.7で「Integer-to-OctetString」という名前で定義されています。これは、ASN.1ベースの構造内のECDSA秘密鍵(x)のエンコードの仕様で使用されます。

bits2octets is not used in standard DSA or ECDSA. We will use it in the specification of deterministic (EC)DSA.


2.4. Signature Generation
2.4. 署名の生成

Signature generation uses a cryptographic hash function H and an input message m. The message is first processed by H, yielding the value H(m), which is a sequence of bits of length hlen. Normally, H is chosen such that its output length hlen is roughly equal to qlen, since the overall security of the signature scheme will depend on the smallest of hlen and qlen; however, the relevant standards support all combinations of hlen and qlen.


The following steps are then applied:


1. H(m) is transformed into an integer modulo q using the bits2int transform and an extra modular reduction:

1. H(m)は、bits2int変換と追加のモジュラー削減を使用して、qを法とした整数に変換されます。

          h = bits2int(H(m)) mod q

As was noted in the description of bits2octets, the extra modular reduction is no more than a conditional subtraction.


2. A random value modulo q, dubbed k, is generated. That value shall not be 0; hence, it lies in the [1, q-1] range. Most of the remainder of this document will revolve around the process used to generate k. In plain DSA or ECDSA, k should be selected through a random selection that chooses a value among the q-1 possible values with uniform probability.

2. qを法とするkと呼ばれる乱数値が生成されます。その値は0であってはなりません。したがって、[1、q-1]の範囲にあります。このドキュメントの残りのほとんどは、kを生成するために使用されるプロセスを中心に展開します。プレーンDSAまたはECDSAでは、ランダムな選択によりkを選択する必要があります。ランダムな選択では、q-1の可能な値の中から一定の確率で値を選択します。

3. A value r (modulo q) is computed from k and the key parameters:

3. 値r(qを法とする)はkと主要なパラメーターから計算されます。

* For DSA:

* DSAの場合:

r = g^k mod p mod q

r = g ^ k mod p mod q

(The exponentiation is performed modulo p, yielding a number between 0 and p-1, which is then further reduced modulo q.)


* For ECDSA: the point kG is computed; its X coordinate (a member of the field over which E is defined) is converted to an integer, which is reduced modulo q, yielding r.

* ECDSAの場合:ポイントkGが計算されます。そのX座標(Eが定義されているフィールドのメンバー)は整数に変換され、qを法として縮小されてrになります。

If r turns out to be zero, a new k should be selected and r computed again (this is an utterly improbable occurrence).


4. The value s (modulo q) is computed:

4. 値s(qを法とする)が計算されます。

          s = (h+x*r)/k mod q

The pair (r, s) is the signature. How a signature is to be encoded is not covered by the DSA and ECDSA standards themselves; a common way is to use a DER-encoded ASN.1 structure (a SEQUENCE of two INTEGERs, for r and s, in that order).


3. Deterministic DSA and ECDSA
3. 確定的DSAおよびECDSA

Deterministic (EC)DSA is the process of generating an (EC)DSA signature over an input message m by using the standard (EC)DSA signature generation process (discussed in the previous section), except that the value k, instead of being randomly generated, is obtained through the process described in this section.


We use the notations described in Section 2.


3.1. Building Blocks
3.1. ビルディングブロック
3.1.1. HMAC
3.1.1. HMAC

HMAC [RFC2104] is a construction of a Message Authentication Code using a hash function and a secret key. Here, we use HMAC with the same hash function H as the one used to process the input message prior to signature generation or verification.

HMAC [RFC2104]は、ハッシュ関数と秘密鍵を使用したメッセージ認証コードの構築です。ここでは、署名の生成または検証の前に入力メッセージを処理するために使用されるものと同じハッシュ関数Hを持つHMACを使用します。

We denote the process of applying HMAC with key K over data V by:




which returns a sequence of bits of length hlen (the output length of the underlying hash function H).


3.2. Generation of k
3.2. kの生成

Given the input message m, the following process is applied:


a. Process m through the hash function H, yielding:

a. ハッシュ関数Hを介してmを処理すると、次のようになります。

h1 = H(m)

h1 = H(m)

(h1 is a sequence of hlen bits).


b. Set:

b. セットする:

V = 0x01 0x01 0x01 ... 0x01

V = 0x01 0x01 0x01 ... 0x01

such that the length of V, in bits, is equal to 8*ceil(hlen/8). For instance, on an octet-based system, if H is SHA-256, then V is set to a sequence of 32 octets of value 1. Note that in this step and all subsequent steps, we use the same H function as the one used in step 'a' to process the input message; this choice will be discussed in more detail in Section 3.6.

Vの長さ(ビット単位)が8 * ceil(hlen / 8)に等しくなるようにします。たとえば、オクテットベースのシステムでは、HがSHA-256の場合、Vは値1の32オクテットのシーケンスに設定されます。このステップと後続のすべてのステップでは、1と同じH関数を使用します。入力メッセージを処理するためにステップ 'a'で使用されます。この選択については、セクション3.6で詳しく説明します。

c. Set:

c. セットする:

K = 0x00 0x00 0x00 ... 0x00

K = 0x00 0x00 0x00 ... 0x00

such that the length of K, in bits, is equal to 8*ceil(hlen/8).

Kの長さ(ビット)が8 * ceil(hlen / 8)に等しくなるようにします。

d. Set:

d. セットする:

          K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1))

where '||' denotes concatenation. In other words, we compute HMAC with key K, over the concatenation of the following, in order: the current value of V, a sequence of eight bits of value 0, the encoding of the (EC)DSA private key x, and the hashed message (possibly truncated and extended as specified by the bits2octets transform). The HMAC result is the new value of K. Note that the private key x is in the [1, q-1] range, hence a proper input for int2octets, yielding rlen bits of output, i.e., an integral number of octets (rlen is a multiple of 8).

ここで '||'連結を示します。つまり、Vの現在の値、値0の8ビットのシーケンス、(EC)DSA秘密鍵xのエンコーディング、およびハッシュされたメッセージ(bits2octets変換で指定されたように切り捨てられ、拡張される可能性があります)。 HMACの結果はKの新しい値です。秘密鍵xは[1、q-1]の範囲にあるため、int2octetsの適切な入力であり、出力のrlenビット、つまりオクテットの整数(rlenは8の倍数です)。

e. Set:

e. セットする:



f. Set:

f. セットする:

          K = HMAC_K(V || 0x01 || int2octets(x) || bits2octets(h1))

Note that the "internal octet" is 0x01 this time.


g. Set:

g. セットする:



h. Apply the following algorithm until a proper value is found for k:

h. kの適切な値が見つかるまで、次のアルゴリズムを適用します。

1. Set T to the empty sequence. The length of T (in bits) is denoted tlen; thus, at that point, tlen = 0.

1. Tを空のシーケンスに設定します。 Tの長さ(ビット単位)はtlenで示されます。したがって、その時点では、tlen = 0です。

2. While tlen < qlen, do the following:

2. tlen <qlenの間に、次のことを行います。



T = T || V

T = T || V

3. Compute:

3. 計算:

k = bits2int(T)

k = bits2int(T)

If that value of k is within the [1,q-1] range, and is suitable for DSA or ECDSA (i.e., it results in an r value that is not 0; see Section 3.4), then the generation of k is finished. The obtained value of k is used in DSA or ECDSA. Otherwise, compute:

そのkの値が[1、q-1]の範囲内にあり、DSAまたはECDSAに適している場合(つまり、r値が0ではない場合。セクション3.4を参照)、kの生成は終了します。 。得られたkの値は、DSAまたはECDSAで使用されます。それ以外の場合は、次を計算します。

K = HMAC_K(V || 0x00)

K = HMAS_K(B || 0x00)



and loop (try to generate a new T, and so on).


Please note that when k is generated from T, the result of bits2int is compared to q, not reduced modulo q. If the value is not between 1 and q-1, the process loops. Performing a simple modular reduction would induce biases that would be detrimental to signature security.


3.3. Alternate Description of the Generation of k
3.3. kの生成の代替説明

The process described in the previous section is actually derived from the "HMAC_DRBG" pseudorandom number generator, described in [SP800-90A] and Annex D of [X9.62]. Using the terminology from [SP800-90A], the generation of k can be described as such:

前のセクションで説明したプロセスは、[SP800-90A]および[X9.62]のAnnex Dで説明されている「HMAC_DRBG」疑似乱数ジェネレータから実際に派生しています。 [SP800-90A]の用語を使用すると、kの生成は次のように説明できます。

a. Instantiate HMAC_DRBG using HMAC parameterized with the same hash function H as the one used for processing the message that is to be signed. Instantiation parameters are:

a. 署名されるメッセージの処理に使用されるものと同じハッシュ関数Hでパラメーター化されたHMACを使用してHMAC_DRBGをインスタンス化します。インスタンス化パラメーターは次のとおりです。

requested_instantiation_security_strength Set this parameter to any value that the HMAC_DRBG implementation will accept, when using H as base hash function.

requested_instantiation_security_strength Hをベースハッシュ関数として使用するときに、HMAC_DRBG実装が受け入れる任意の値にこのパラメーターを設定します。

prediction_resistance_flag Set this parameter to "false".


personalization_string Set this parameter to "Null" (the empty bit sequence).

personalization_stringこのパラメーターを "Null"(空のビットシーケンス)に設定します。

entropy_input Use int2octets(x) as entropy string.


nonce Use bits2octets(H(m)) as nonce.


Note that the last two parameters are not parameters to the HMAC_DRBG instantiation function per se; instead, those values are requested from the internal Get_entropy_input function during instantiation. For deterministic (EC)DSA, we want HMAC_DRBG to run with the entropy string and nonce that we specify, without accessing an actual entropy source.


b. Generate a candidate value for k by requesting qlen bits from HMAC_DRBG and converting the resulting bits into an integer with the bits2int transform. Repeat this step until a value is obtained, which is non-zero, less than q, and suitable for (EC)DSA (see Section 3.4).

b. HMAC_DRBGからqlenビットを要求し、bits2int変換を使用して結果のビットを整数に変換することにより、kの候補値を生成します。ゼロではなく、q未満で(EC)DSAに適した値が得られるまで、この手順を繰り返します(セクション3.4を参照)。

Note that we instantiate a new HMAC_DRBG instance for each signature generation process. There is no "personalization string" and no "additional input" when generating bits. The reseed function of HMAC_DRBG is never invoked, neither externally nor as a consequence of the internal HMAC_DRBG processing.

署名生成プロセスごとに新しいHMAC_DRBGインスタンスをインスタンス化することに注意してください。ビットを生成するとき、「パーソナライゼーション文字列」も「追加入力」もありません。 HMAC_DRBGの再シード機能は、外部的にも内部HMAC_DRBG処理の結果としても呼び出されることはありません。

As shown above, we use the encoding of the private key as "entropy string" and the hashed message (truncated and expanded by bits2octets) as "nonce". In HMAC_DRBG, the entropy string and nonce are simply concatenated into the initial seed; hence, the split between "entropy" and "nonce" is quite arbitrary. Using qlen bits for each ought to be compatible with most HMAC_DRBG implementation input requirements.

上記のように、秘密鍵のエンコーディングを「エントロピー文字列」として使用し、ハッシュされたメッセージ(ビット2オクテットで切り捨てられて拡張された)を「ノンス」として使用します。 HMAC_DRBGでは、エントロピー文字列とノンスが単純に連結されて初期シードになります。したがって、「エントロピー」と「ノンス」の分割は非常に恣意的です。それぞれにqlenビットを使用することは、ほとんどのHMAC_DRBG実装入力要件と互換性があるはずです。

3.4. Usage Notes
3.4. 使用上の注意

With DSA or ECDSA, the value k is used to compute the first half of the signature, dubbed r (see Section 2.4). The DSA and ECDSA standards mandate that, if r is zero, then a new k should be selected. In that situation, this document specifies that the value k is "unsuitable", and the generation process shall keep on looping.

DSAまたはECDSAでは、値kは署名の前半を計算するために使用され、rと呼ばれます(セクション2.4を参照)。 DSAおよびECDSA規格では、rがゼロの場合、新しいkを選択する必要があります。そのような状況では、このドキュメントでは、値kが「不適切」であり、生成プロセスがループし続けることを指定しています。

This occurrence is utterly improbable. Actually, it would require considerable computational effort (similar to breaking preimage resistance of the hash function) to find a private key and a message that lead to a zero value for r; hitting such a case by pure chance is thus deemed implausible, and an attacker cannot force it with carefully crafted messages. In practice, such a code path will not be triggered and thus can be implemented with little optimization.


3.5. Rationale
3.5. 根拠

The process described in the previous sections mimics the "Approved" generation process of k described in Annex D of [X9.62], with the "HMAC_DRBG" pseudorandom number generator. The main difference is that we use the concatenation of the private key x and the hashed message H(m) as the pseudorandom number generator (PRNG) seed. If using a "security level" of n bits, then HMAC_DRBG should be used with seed entropy at least n+64 bits; however, the key x should also have been generated with that much entropy, and the length of x is qlen, which is at least equal to 2*n and thus larger than n+64 (DSA and ECDSA, as specified by the standards, require qlen >= 160). It can then be argued that deterministic ECDSA fulfills the entropy requirements of Annex D of [X9.62].

前のセクションで説明したプロセスは、[X9.62]の付録Dで説明されているkの「承認済み」生成プロセスを模倣し、「HMAC_DRBG」疑似乱数ジェネレータを備えています。主な違いは、秘密鍵xとハッシュされたメッセージH(m)の連結を疑似乱数ジェネレーター(PRNG)シードとして使用することです。 nビットの「セキュリティレベル」を使用する場合、HMAC_DRBGは少なくともn + 64ビットのシードエントロピーで使用する必要があります。ただし、キーxも同じくらいのエントロピーで生成されている必要があり、xの長さはqlenです。これは、少なくとも2 * nに等しく、n + 64よりも大きい(DSAおよびECDSA、規格で指定されているとおり)、 qlen> = 160が必要です)。次に、決定論的ECDSAは、[X9.62]のAnnex Dのエントロピー要件を満たしていると主張することができます。

We use bits2octets(H(m)) instead of H(m) in order to ease integration. Indeed, many existing signature systems offload the message hashing; the signature engine (which has access to the private key) receives only H(m). In some applications, where data bandwidth is constrained, only the first qlen bits of H(m) are transferred to the signature engine, on the basis that the bits2int transform will ignore subsequent bits anyway. Possibly, in some systems, the truncated H(m) could be externally reduced modulo q, since that is the first thing that (EC)DSA performs on the hashed message. With the definition of bits2octets, deterministic (EC)DSA can be applied with the same input.

統合を容易にするために、H(m)の代わりにbits2octets(H(m))を使用します。実際、多くの既存の署名システムはメッセージハッシュをオフロードします。署名エンジン(秘密鍵にアクセスできる)は、H(m)のみを受け取ります。データ帯域幅が制限されている一部のアプリケーションでは、bits2int変換が後続のビットを無視することに基づいて、H(m)の最初のqlenビットのみが署名エンジンに転送されます。おそらく、一部のシステムでは、切り捨てられたH(m)は、(EC)DSAがハッシュされたメッセージに対して最初に実行するものであるため、qを法として外部的に削減できます。 bits2octetsの定義により、確定的(EC)DSAを同じ入力に適用できます。

3.6. Variants
3.6. バリアント

Many parts of the specification of deterministic (EC)DSA are quite arbitrary. It is possible to define variants that are NOT "deterministic (EC)DSA" but that may nonetheless be useful in some contexts:

確定的(EC)DSAの仕様の多くの部分は非常に恣意的です。 「確定的(EC)DSA」ではないバリアントを定義することは可能ですが、それでも一部のコンテキストでは役立ちます。

o It is possible to use H(m) directly, instead of bits2octets(H(m)), as part of the HMAC input. As explained in Section 3.5, we use bits2octets(H(m)) in order to ease integration into systems that already use an (EC)DSA signature engine by sending it an already-truncated hash value. Using the whole H(m) does not introduce any vulnerability.

o HMAC入力の一部として、bits2octets(H(m))の代わりにH(m)を直接使用することが可能です。セクション3.5で説明したように、すでに切り捨てられたハッシュ値を送信することにより、(EC)DSA署名エンジンをすでに使用しているシステムへの統合を容易にするために、bits2octets(H(m))を使用します。 H(m)全体を使用しても、脆弱性は発生しません。

o Additional data may be added to the input of HMAC, concatenated after bits2octets(H(m)):

o 追加データは、HMACの入力に追加され、bits2octets(H(m))の後に連結されます。

         K = HMAC_K(V || 0x00 || int2octets(x) || bits2octets(h1) || k')

A use case may be a protocol that requires a non-deterministic signature algorithm on a system that does not have access to a high-quality random source. It suffices that the additional data k' is non-repeating (e.g., a signature counter or a monotonic clock) to ensure "random-looking" signatures are indistinguishable, in a cryptographic way, from plain (EC)DSA signatures. In [SP800-90A] terminology, k' is the "additional

ユースケースは、高品質のランダムソースにアクセスできないシステムで非決定論的な署名アルゴリズムを必要とするプロトコルである場合があります。 「ランダムに見える」シグネチャがプレーンな(EC)DSAシグネチャと暗号的に区別できないことを保証するには、追加データk 'が繰り返されない(たとえば、シグネチャカウンターまたは単調クロック)ことで十分です。 [SP800-90A]の用語では、k 'は「追加の

input" that can be set as a parameter when generating pseudorandom bits. This variant can be thought of as a "strengthening" of the randomness of the source of the additional data k'.

疑似ランダムビットを生成するときにパラメーターとして設定できる入力。このバリアントは、追加データk 'のソースのランダム性の「強化」と考えることができます。

o Instead of using x (the private key) as input to HMAC, it is possible to use additional secret data, stored along with the private key with the same security measures. The entropy of that additional data SHALL be at least n bits, preferably n+64 bits or more, where n is the target security level. Having additional secret data may help in formally proving the security of derandomization, but it implies an extra storage cost and incompatibility with already-generated (EC)DSA private keys.

o HMACへの入力としてx(秘密鍵)を使用する代わりに、同じセキュリティ対策で秘密鍵とともに保存された追加の秘密データを使用することが可能です。その追加データのエントロピーは、少なくともnビット、できればn + 64ビット以上である必要があります(nはターゲットセキュリティレベル)。追加の秘密データがあることは、ランダム化解除のセキュリティを正式に証明するのに役立ちますが、追加のストレージコストと、すでに生成された(EC)DSA秘密鍵との非互換性を意味します。

o Similarly, the private key could be a value z, from which both x (the "private key" in the plain (EC)DSA sense) and another value x', to be used as input to HMAC in the generation of k, would be derived through a suitable Pseudorandom Function (PRF) (such as HMAC_DRBG). This would keep private key storage requirements to a minimum while providing a more easily proven security, but it would impact private key generation and would not be compatible with already-generated key pairs.

o 同様に、秘密鍵は値zであり、x(プレーン(EC)DSAの意味での「秘密鍵」)と別の値x 'の両方が、kの生成でHMACへの入力として使用されます。適切な疑似ランダム関数(PRF)(HMAC_DRBGなど)を介して導出される。これにより、より簡単に証明できるセキュリティを提供しながら、秘密キーのストレージ要件を最小限に抑えることができますが、秘密キーの生成に影響を与え、すでに生成されたキーペアとの互換性がなくなります。

o In this document, we use the same hash function H for processing the input message and as a parameter to HMAC. Two distinct hash functions could be used, provided that both are adequately secure. The overall security will be limited by the weaker of the two hash functions, i.e., the one with the smaller output. Using a specific, constant hash function for HMAC may be useful for constrained implementations that accept externally hashed messages, regardless of what hash function was used for that, but have resources for implementing only one hash function for HMAC.

o このドキュメントでは、入力メッセージの処理とHMACへのパラメーターとして同じハッシュ関数Hを使用します。両方が十分に安全であれば、2つの異なるハッシュ関数を使用できます。全体的なセキュリティは、2つのハッシュ関数のうち弱い方、つまり出力が小さい方によって制限されます。 HMACに特定の定数ハッシュ関数を使用すると、どのハッシュ関数が使用されたかに関係なく、外部でハッシュされたメッセージを受け入れるが、HMACにハッシュ関数を1つだけ実装するためのリソースがある制約のある実装に役立ちます。

The main disadvantage of any variant is that it ceases to be verifiable against the test vectors published in this document.


4. Security Considerations
4. セキュリティに関する考慮事項

Proper implementation and usage of a cryptographic signature algorithm require taking into account many parameters. In particular, private key generation, storage, access control, and disposal are sensitive operations, which this document does not address in any way. Deterministic (EC)DSA shows how to achieve the security characteristics of a standard DSA or ECDSA signature scheme while removing the need for a source of strong randomness, or even any source of randomness, during signature generation.

暗号化署名アルゴリズムを適切に実装して使用するには、多くのパラメーターを考慮する必要があります。特に、秘密鍵の生成、保存、アクセス制御、および廃棄は機密性の高い操作であり、このドキュメントではこれについては触れていません。 Deterministic(EC)DSAは、標準のDSAまたはECDSA署名方式のセキュリティ特性を達成しながら、署名の生成時に強力なランダム性のソースまたはランダム性のソースの必要性を排除する方法を示します。

Private key generation, however, absolutely requires such a strongly random source. In situations where deterministic (EC)DSA is to be used due to the lack of an appropriate source of randomness, one must assume that the private key has been generated externally and imported into the signature generation system or was generated in a context where randomness was available. For instance, one can imagine a smartcard that generates its private key while still in the factory under controlled environmental conditions, but for which random data generation cannot be guaranteed once deployed in the field, when physically in the hands of potential attackers.


Both removal of the random source requirement and the ability to test an implementation against test vectors enhance security of DSA and ECDSA signer implementations, in that they help avoid hard-to-test failure conditions. Deterministic signature schemes may also help in other situations, e.g., to avoid spurious duplicates, when the same data element is signed several times with the same key: with a deterministic signature scheme, the same signature is generated every time, making duplicate detection much easier.

ランダムソース要件の削除と、テストベクタに対して実装をテストする機能の両方が、テストが困難な障害状態を回避するのに役立つという点で、DSAおよびECDSA署名者実装のセキュリティを強化します。確定的署名方式は他の状況でも役立つ場合があります。たとえば、同じデータ要素が同じキーで何度も署名されている場合、偽の重複を避けることができます。確定的署名方式では、毎回同じ署名が生成され、重複検出がはるかに簡単になります。 。

Conversely, lack of randomization may have adverse effects in some advanced protocols, e.g., related to anonymity in some voting schemes. As a rule of thumb, deterministic DSA or ECDSA can be used in lieu of the genuine DSA or ECDSA, with no additional security issues, if the overall protocol would tolerate another deterministic signature scheme, in particular RSA as specified in PKCS #1 [RFC3447] (with "type 1" padding, not PSS) or ISO 9796-2 [ISO-9796-2]. The list of protocols in which deterministic DSA or ECDSA is appropriate includes Transport Layer Security (TLS) [RFC5246], the Secure SHell (SSH) Protocol [RFC4251], Cryptographic Message Syntax (CMS) [RFC5652] and derivatives, X.509 public key infrastructures [RFC5280], and many others.

逆に、ランダム化の欠如は、たとえば一部の投票スキームの匿名性に関連するなど、一部の高度なプロトコルに悪影響を与える可能性があります。経験則として、プロトコル全体が別の確定的署名スキーム、特にPKCS#1 [RFC3447で指定されているRSAを許容する場合、追加のセキュリティ問題なしで、本物のDSAまたはECDSAの代わりに確定的DSAまたはECDSAを使用できます。 ](PSSではなく「タイプ1」のパディング付き)またはISO 9796-2 [ISO-9796-2]。確定的DSAまたはECDSAが適切なプロトコルのリストには、トランスポート層セキュリティ(TLS)[RFC5246]、セキュアシェル(SSH)プロトコル[RFC4251]、暗号化メッセージ構文(CMS)[RFC5652]および派生物、X.509パブリックが含まれます。主要インフラストラクチャ[RFC5280]、およびその他多数。

The construction described in this document is known as a "derandomization". This has been proposed for various signature schemes. Security relies on whether the generation of k is indistinguishable from the output of a random oracle. Roughly speaking, HMAC_DRBG is secure in that role as long as HMAC behaves as a PRF (Pseudorandom Function). For details on the security of HMAC and HMAC_DRBG, please refer to [H2008] and [B2006]. For a more formal treatment of derandomization, see [LN2009].

このドキュメントで説明する構成は、「ランダム化」と呼ばれます。これは、さまざまな署名方式に対して提案されています。セキュリティは、kの生成がランダムオラクルの出力と区別できないかどうかに依存します。大まかに言えば、HMACがPRF(疑似ランダム関数)として動作する限り、HMAC_DRBGはその役割で安全です。 HMACおよびHMAC_DRBGのセキュリティの詳細については、[H2008]および[B2006]を参照してください。非ランダム化のより正式な扱いについては、[LN2009]を参照してください。

One remaining issue with deterministic (EC)DSA, as presented in this document, is the "double use" of the private key x, both as the private key in the signature generation algorithm itself and as input to the HMAC_DRBG-based pseudorandom oracle for producing the k value. This requires HMAC_DRBG to keep on being a random oracle, even when the public key (which is computed from x) is also known. Given the lack of common structure between HMAC and discrete logarithms, this seems a reasonable assumption.

このドキュメントで示されているように、確定的(EC)DSAの残りの問題の1つは、秘密鍵xの「二重使用」です。これは、署名生成アルゴリズム自体の秘密鍵として、およびHMAC_DRBGベースの擬似ランダムオラクルへの入力としての両方です。 k値を生成します。これには、公開鍵(xから計算される)もわかっている場合でも、ランダムなオラクルであり続けるためにHMAC_DRBGが必要です。 HMACと離散対数の間に共通の構造がないことを考えると、これは妥当な仮定のようです。

Side-channel attacks are an important consideration whenever an attacker can accurately measure aspects of an implementation such as the length of time that it takes to perform a signing operation or the power consumed at each point of a signing operation. The determinism of the algorithms described in this note may be useful to an attacker in some forms of side-channel attacks, so implementations SHOULD use defensive measures to avoid leaking the private key through a side channel.


5. Intellectual Property Status
5. 知的財産の状況

To the best of our knowledge, deterministic (EC)DSA is not covered by any active patent. The paper [BDLSY2011] points to two independent publications of the idea of derandomization by Barwood and Wigley, both in early 1997, and also to a patent application by Naccache, M'Raihi, and Levy-dit-Vehel a few months later [NML1997], but the application was withdrawn in 2003. We are not aware of any other patent on the subject.

私たちの知る限りでは、確定的(EC)DSAは有効な特許の対象ではありません。論文[BDLSY2011]は、BarwoodとWigleyによる非ランダム化のアイデアに関する2つの独立した出版物を、両方とも1997年初頭に指摘し、さらにNaccache、M'Raihi、およびLevy-dit-Vehelによる数か月後の特許出願を指摘しています[NML1997 ]ですが、出願は2003年に取り下げられました。この件に関する他の特許については知りません。

6. References
6. 参考文献
6.1. Normative References
6.1. 引用文献

[FIPS-186-4] National Institute of Standards and Technology, "Digital Signature Standard (DSS)", Federal Information Processing Standards Publication (FIPS PUB) 186-4, July 2013.

[FIPS-186-4]米国国立標準技術研究所、「デジタル署名標準(DSS)」、連邦情報処理標準出版物(FIPS PUB)186-4、2013年7月。

[RFC2104] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-Hashing for Message Authentication", RFC 2104, February 1997.

[RFC2104] Krawczyk、H.、Bellare、M。、およびR. Canetti、「HMAC:Keyed-Hashing for Message Authentication」、RFC 2104、1997年2月。

[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997.

[RFC2119] Bradner、S。、「要件レベルを示すためにRFCで使用するキーワード」、BCP 14、RFC 2119、1997年3月。

[SEC1] Certicom Research, "SEC 1: Elliptic Curve Cryptography (Version 2.0)", May 2009.

[SEC1] Certicom Research、「SEC 1:Elliptic Curve Cryptography(Version 2.0)」、2009年5月。

[SP800-90A] National Institute of Standards and Technology, "Recommendation for Random Number Generation Using Deterministic Random Bit Generators (Revised)", NIST Special Publication 800-90A, January 2012.

[SP800-90A]米国国立標準技術研究所、「確定的ランダムビットジェネレーターを使用した乱数生成の推奨(改訂版)」、NIST Special Publication 800-90A、2012年1月。

[X9.62] American National Standards Institute, "Public Key Cryptography for the Financial Services Industry: The Elliptic Curve Digital Signature Algorithm (ECDSA)", ANSI X9.62-2005, November 2005.

[X9.62] American National Standards Institute、「金融サービス業界の公開鍵暗号化:楕円曲線デジタル署名アルゴリズム(ECDSA)」、ANSI X9.62-2005、2005年11月。

6.2. Informative References
6.2. 参考引用

[B2006] Bellare, M., "New Proofs for NMAC and HMAC: Security without Collision-Resistance", Crypto 2006, LNCS 4117, August 2006.

[B2006] Bellare、M。、「NMACとHMACの新しい証明:衝突防止なしのセキュリティ」、Crypto 2006、LNCS 4117、2006年8月。

[BDLSY2011] Bernstein, D., Duif, N., Lange, T., Schwabe, P., and B. Yang, "High-speed high-security signatures", Cryptology ePrint Archive Report 2011/368, September 2011.

[BDLSY2011] Bernstein、D.、Duif、N.、Lange、T.、Schwabe、P。、およびB. Yang、「高速高セキュリティ署名」、Cryptology ePrint Archive Report 2011 / 368、2011年9月。

[FIPS-180-4] National Institute of Standards and Technology, "Secure Hash Standard (SHS)", Federal Information Processing Standards Publication (FIPS PUB) 180-4, March 2012.

[FIPS-180-4]米国国立標準技術研究所、「Secure Hash Standard(SHS)」、連邦情報処理標準出版物(FIPS PUB)180-4、2012年3月。

[H2008] Hirose, S., "Security Analysis of DRBG Using HMAC in NIST SP 800-90", Information Security Applications (WISA 2008), LNCS 5379, September 2008.

[H2008] Hirose、S。、「NIST SP 800-90でHMACを使用したDRBGのセキュリティ分析」、情報セキュリティアプリケーション(WISA 2008)、LNCS 5379、2008年9月。

[ISO-9796-2] International Organization for Standardization, "Information technology -- Security techniques -- Digital signature schemes giving message recovery -- Part 2: Integer factorization based mechanisms", ISO/ IEC 9796-2:2010, December 2010.

[ISO-9796-2]国際標準化機構、「情報技術-セキュリティ技術-メッセージ回復を提供するデジタル署名方式-パート2:整数分解ベースのメカニズム」、ISO / IEC 9796-2:2010、2010年12月。

[LN2009] Leurent, G. and P. Nguyen, "How Risky is the Random-Oracle Model?", Cryptology ePrint Archive Report 2008/ 441, July 2009, <>.

[LN2009] Leurent、G。およびP. Nguyen、「ランダムオラクルモデルはどのように危険ですか?」、Cryptology ePrint Archive Report 2008 / 441、2009年7月、<> 。


[NML1997] Naccache、D.、M'Raihi、D。、およびF. Levy-dit-Vehel、「ランダムな描画を必要とする暗号システムのハッシュコーディング関数に基づく疑似ランダムジェネレータ」、WIPO特許公開WO / 1998 / 051038、1998年5月。

[RFC3447] Jonsson, J. and B. Kaliski, "Public-Key Cryptography Standards (PKCS) #1: RSA Cryptography Specifications Version 2.1", RFC 3447, February 2003.

[RFC3447] Jonsson、J。およびB. Kaliski、「Public-Key Cryptography Standards(PKCS)#1:RSA Cryptography Specifications Version 2.1」、RFC 3447、2003年2月。

[RFC4251] Ylonen, T. and C. Lonvick, "The Secure Shell (SSH) Protocol Architecture", RFC 4251, January 2006.

[RFC4251] Ylonen、T。およびC. Lonvick、「The Secure Shell(SSH)Protocol Architecture」、RFC 4251、2006年1月。

[RFC5246] Dierks, T. and E. Rescorla, "The Transport Layer Security (TLS) Protocol Version 1.2", RFC 5246, August 2008.

[RFC5246] Dierks、T。およびE. Rescorla、「The Transport Layer Security(TLS)Protocol Version 1.2」、RFC 5246、2008年8月。

[RFC5280] Cooper, D., Santesson, S., Farrell, S., Boeyen, S., Housley, R., and W. Polk, "Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile", RFC 5280, May 2008.

[RFC5280] Cooper、D.、Santesson、S.、Farrell、S.、Boeyen、S.、Housley、R。、およびW. Polk、「Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List(CRL)Profile "、RFC 5280、2008年5月。

[RFC5652] Housley, R., "Cryptographic Message Syntax (CMS)", STD 70, RFC 5652, September 2009.

[RFC5652] Housley、R。、「Cryptographic Message Syntax(CMS)」、STD 70、RFC 5652、2009年9月。

Appendix A. Examples
A.1. Detailed Example
A.1. 詳細な例

We detail here the intermediate values obtained during the generation of k on an example message and key. We use a binary curve because that specific curve is standard and has a group order length (qlen) that is not a multiple of 8; this illustrates the fine details of how conversions are performed between integers and bit sequences.


A.1.1. Key Pair
A.1.1. キーペア

We consider ECDSA on the curve K-163 described in [FIPS-186-4] (also known as "ansix9t163k1" in [X9.62]). The curve is defined over a field GF(2^163): field elements are encoded into 163-bit strings. The order of the conventional base point is the prime value:

[FIPS-186-4]で説明されている曲線K-163([X9.62]では「ansix9t163k1」とも呼ばれる)でECDSAを検討します。曲線はフィールドGF(2 ^ 163)で定義されます。フィールド要素は163ビットの文字列にエンコードされます。従来のベースポイントの次数は素数です。

      q = 0x4000000000000000000020108A2E0CC0D99F8A5EF

which has length qlen = 163 bits.

長さqlen = 163ビットです。

Our private key is:


      x = 0x09A4D6792295A7F730FC3F2B49CBC0F62E862272F

The corresponding public key is the curve point U = xG. This point has two coordinates, which are elements of the field GF(2^163). These elements can be converted to integers using the procedure described in Section A.5.6 of [X9.62], yielding the two public point coordinates:

対応する公開鍵は、曲線ポイントU = xGです。このポイントには、フィールドGF(2 ^ 163)の要素である2つの座標があります。これらの要素は、[X9.62]のセクションA.5.6で説明されている手順を使用して整数に変換でき、2つのパブリックポイント座標が得られます。

      Ux = 0x79AEE090DB05EC252D5CB4452F356BE198A4FF96F
      Uy = 0x782E29634DDC9A31EF40386E896BAA18B53AFA5A3
A.1.2. Generation of k
A.1.2. kの生成

In this example, we use the hash function SHA-256 [FIPS-180-4]. The input message is the UTF-8 encoding of the string "sample" (6 octets, i.e., 48 bits).

この例では、ハッシュ関数SHA-256 [FIPS-180-4]を使用します。入力メッセージは、文字列「サンプル」のUTF-8エンコーディングです(6オクテット、つまり48ビット)。

The hashed input message h1 = SHA-256(m) is:

ハッシュされた入力メッセージh1 = SHA-256(m)は次のとおりです。

h1 AF 2B DB E1 AA 9B 6E C1 E2 AD E1 D6 94 F4 1F C7 1A 83 1D 02 68 E9 89 15 62 11 3D 8A 62 AD D1 BF

h1 AF 2B DB E1 AA 9B 6E C1 E2 AD E1 D6 94 F4 1F C7 1A 83 1D 02 68 E9 89 15 62 11 3D 8A 62 AD D1 BF

(32 octets; each octet value is listed in hexadecimal notation).


We convert the private key x to a sequence of octets using the int2octets transform:


int2octets(x) 00 9A 4D 67 92 29 5A 7F 73 0F C3 F2 B4 9C BC 0F 62 E8 62 27 2F

インタクトTES(X)00 9A 4D 67 92 29 5A 7F 73 0F C3 F2 B4 9C BC 0F 62 E8 62 27 2F

Note: Although the specific value of x would numerically fit in 160 bits, i.e., 20 octets, we still encode x into 21 octets, because the encoding length is driven by the length of q, which is 163 bits.


We also truncate and/or expand the hashed message using bits2octets:


bits2octets(h1) 01 79 5E DF 0D 54 DB 76 0F 15 6D 0D AC 04 C0 32 2B 3A 20 42 24

ビット2オクテット(h1)01 79 5E DF 0D 54 DB 76 0F 15 6D 0D AC 04 C0 32 2B 3A 20 42 24

The steps b to g (see Section 3.2) then compute the values for the K and V variables. These variables are sequences of 256 bits (the hash function output length, rounded up to a multiple of 8). We reproduce here the successive values:


V after step b: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01

ステップbの後のV:01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01

K after step c: 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

ステップcの後のK:00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00

K after step d: 09 99 9A 9B FE F9 72 D3 34 69 11 88 3F AD 79 51 D2 3F 2C 8B 47 F4 20 22 2D 11 71 EE EE AC 5A B8

ステップdの後のK:09 99 9A 9B FE F9 72 D3 34 69 11 88 3F AD 79 51 D2 3F 2C 8B 47 F4 20 22 2D 11 71 EE EE AC 5A B8

V after step e: D5 F4 03 0F 75 5E E8 6A A1 0B BA 8C 09 DF 11 4F F6 B6 11 1C 23 85 00 D1 3C 73 43 A8 C0 1B EC F7

ステップeの後のV:D5 F4 03 0F 75 5E E8 6A A1 0B BA 8C 09 DF 11 4F F6 B6 11 1C 23 85 00 D1 3C 73 43 A8 C0 1B EC F7

K after step f: 0C F2 FE 96 D5 61 9C 9E F5 3C B7 41 7D 49 D3 7E A6 8A 4F FE D0 D7 E6 23 E3 86 89 28 99 11 BD 57

ステップfの後のK:0C F2 FE 96 D5 61 9C 9E F5 3C B7 41 7D 49 D3 7E A6 8A 4F FE D0 D7 E6 23 E3 86 89 28 99 11 BD 57

V after step g: 78 34 57 C1 CF 31 48 A8 F2 A9 AE 73 ED 47 2F A9 8E D9 CD 92 5D 8E 96 4C E0 76 4D EF 3F 84 2B 9A

ステップg後のV:78 34 57 C1 CF 31 48 A8 F2 A9 AE 73 ED 47 2F A9 8E D9 CD 92 5D 8E 96 4C E0 76 4D EF 3F 84 2B 9A

In step h, we perform the final loop. Since we use HMAC with SHA-256, which produces 256 bits worth of output, and we need only 163 bits for T, a single HMAC invocation yields the following T:

ステップhでは、最後のループを実行します。 SHA-256でHMACを使用して256ビット相当の出力を生成し、Tに必要なのは163ビットだけなので、1回のHMAC呼び出しで次のTが得られます。

T (first try) 93 05 A4 6D E7 FF 8E B1 07 19 4D EB D3 FD 48 AA 20 D5 E7 65 6C BE 0E A6 9D 2A 8D 4E 7C 67 31 4A

T(最初の試行)93 05 A4 6D E7 FF 8E B1 07 19 4D EB D3 FD 48 AA 20 D5 E7 65 6C BE 0E A6 9D 2A 8D 4E 7C 67 31 4A

which, when converted to an integer with bits2int, yields a first candidate for k:


      k1 = 0x4982D236F3FFC758838CA6F5E9FEA455106AF3B2B

Since that value is greater than q-1, we have to loop. This first entails computing new values for K and V:


new K 75 CB 5C 05 B2 A7 8C 3D 81 DF 12 D7 4D 7B E0 A0 E9 4A B1 98 15 78 1D 4D 8E 29 02 A7 9D 0A 66 99

新しいK 75 CB 5C 05 B2 A7 8C 3D 81 DF 12 D7 4D 7B E0 A0 E9 4A B1 98 15 78 1D 4D 8E 29 02 A7 9D 0A 66 99

new V DC B9 CA 12 61 07 A9 C2 7C E7 7B A5 8E A8 71 C8 C9 12 D8 35 EA DD C3 05 F2 44 5D 88 F6 6C 4C 43

新しいV DC B9 CA 12 61 07 A9 C2 7C E7 7B A5 8E A8 71 C8 C9 12 D8 35 EA DD C3 05 F2 44 5D 88 F6 6C 4C 43

then a new T:


T (second try) C7 0C 78 60 8A 3B 5B E9 28 9B E9 0E F6 E8 1A 9E 2C 15 16 D5 75 1D 2F 75 F5 00 33 E4 5F 73 BD EB

T(2回目の試行)C7 0C 78 60 8A 3B 5B E9 28 9B E9 0E F6 E8 1A 9E 2C 15 16 D5 75 1D 2F 75 F5 00 33 E4 5F 73 BD EB

and a new candidate for k:


      k2 = 0x63863C30451DADF4944DF4877B740D4F160A8B6AB

Since k2 is also greater than q-1, we loop again:


new K (2) 0A 5A 64 B9 9C 05 95 20 10 36 86 CB 6F 36 BC FC A7 88 EB 3B CF 69 BA 66 A5 BB 08 0B 05 93 BA 53

Kなし(A)0A 5A 64 B9 9C 05 95 20 10 36 86 CB 6F 36 BC FC A7 88 EB 3B CF 69 BA 66 A5 BB 08 0B 05 93 BA 53

new V (2) 0B 3B 19 68 11 B1 9F 6C 6F 72 9C 43 F3 5B CF 0D FD 72 5F 17 CA 34 30 E8 72 14 53 E5 55 50 A1 8F

新しいV(2)0B 3B 19 68 11 B1 9F 6C 6F 72 9C 43 F3 5B CF 0D FD 72 5F 17 CA 34 30 E8 72 14 53 E5 55 50 A1 8F

T (third try) 47 5E 80 E9 92 14 05 67 FC C3 A5 0D AB 90 FE 84 BC D7 BB 03 63 8E 9C 46 56 A0 6F 37 F6 50 8A 7C

T(3回目の試行)47 5E 80 E9 92 14 05 67 FC C3 A5 0D AB 90 FE 84 BC D7 BB 03 63 8E 9C 46 56 A0 6F 37 F6 50 8A 7C

and we finally get an acceptable value for k:


      k = 0x23AF4074C90A02B3FE61D286D5C87F425E6BDD81B
A.1.3. Signature
A.1.3. 署名

With our private key and the value of k that we just generated, we can now compute the signature using the standard ECDSA mechanisms. First, the point kG is computed, and the X coordinate of that point is converted to an integer and then reduced modulo q, yielding the first signature half:


      r = 0x113A63990598A3828C407C0F4D2438D990DF99A7F

which we use, together with x (the private key), k (which we computed above), and h = bits2int(h1), to compute the second signature half:

これをx(秘密鍵)、k(上記で計算)、およびh = bits2int(h1)とともに使用して、2番目の署名の半分を計算します。

      s = 0x1313A2E03F5412DDB296A22E2C455335545672D9F

An ECDSA signature is a pair of integers. In many protocols that require a signature to be a sequence of bits (or octets), it is customary to encode the signature as an ASN.1 SEQUENCE of two INTEGER values, with DER rules. This results in the following 48-octet signature:

ECDSA署名は整数のペアです。一連のビット(またはオクテット)である署名を必要とする多くのプロトコルでは、DER規則を使用して、署名を2つのINTEGER値のASN.1 SEQUENCEとしてエンコードするのが通例です。これにより、次の48オクテットの署名が生成されます。

30 2E 02 15 01 13 A6 39 90 59 8A 38 28 C4 07 C0 F4 D2 43 8D 99 0D F9 9A 7F 02 15 01 31 3A 2E 03 F5 41 2D DB 29 6A 22 E2 C4 55 33 55 45 67 2D 9F

302Е02 15 01 13Ашзя90 598А38 28Цч07 0ФчД2чз8Дяя0ДФяЯАЩФ02 15 01 31ЗА2E 03 F5 41 2D DB 29 6A 22 E2 C4 55 33 55 45 67 2D 9F

A.2. Test Vectors
A.2. テストベクトル

In the following sections, we give test vectors for various key sizes and hash functions, both for DSA and ECDSA.


All numbers are given in hexadecimal notation. Each signature consists of two integers, named r and s; many implementations will encode those integers into a single ASN.1 structure or with some other encoding convention, which is outside of the scope of this document. We also show the k value used internally.


For every key, we list ten signatures, corresponding to two distinct input messages, and five of the SHA [FIPS-180-4] functions: SHA-1, SHA-224, SHA-256, SHA-384, and SHA-512. The two input messages are the UTF-8 encoding of the strings "sample" and "test" (without the quotes), of length 48 and 32 bits, respectively.

すべてのキーについて、2つの異なる入力メッセージに対応する10個の署名と、5個のSHA [FIPS-180-4]関数(SHA-1、SHA-224、SHA-256、SHA-384、SHA-512)をリストします。 2つの入力メッセージは、文字列 "sample"および "test"(引用符なし)のUTF-8エンコーディングで、それぞれ48ビットと32ビットです。

The ECDSA examples use the standard curves described in [FIPS-186-4].


A.2.1. DSA, 1024 Bits
A.2.1. DSA、1024ビット

Key pair:


key parameters:


   p = 86F5CA03DCFEB225063FF830A0C769B9DD9D6153AD91D7CE27F787C43278B447
   q = 996F967F6C8E388D9E28D01E205FBA957A5698B1
   g = 07B0F92546150B62514BB771E2A0C0CE387F03BDA6C56B505209FF25FD3C133D

private key:


   x = 411602CB19A6CCC34494D79D98EF1E7ED5AF25F7

public key:


   y = 5DF5E01DED31D0297E274E1691C192FE5868FEF9E19A84776454B100CF16F653



   With SHA-1, message = "sample":
   k = 7BDB6B0FF756E1BB5D53583EF979082F9AD5BD5B
   r = 2E1A0C2562B2912CAAF89186FB0F42001585DA55
   s = 29EFB6B0AFF2D7A68EB70CA313022253B9A88DF5
   With SHA-224, message = "sample":
   k = 562097C06782D60C3037BA7BE104774344687649
   r = 4BC3B686AEA70145856814A6F1BB53346F02101E
   s = 410697B92295D994D21EDD2F4ADA85566F6F94C1
   With SHA-256, message = "sample":
   k = 519BA0546D0C39202A7D34D7DFA5E760B318BCFB
   r = 81F2F5850BE5BC123C43F71A3033E9384611C545
   s = 4CDD914B65EB6C66A8AAAD27299BEE6B035F5E89
   With SHA-384, message = "sample":
   k = 95897CD7BBB944AA932DBC579C1C09EB6FCFC595
   r = 07F2108557EE0E3921BC1774F1CA9B410B4CE65A
   s = 54DF70456C86FAC10FAB47C1949AB83F2C6F7595
   With SHA-512, message = "sample":
   k = 09ECE7CA27D0F5A4DD4E556C9DF1D21D28104F8B
   r = 16C3491F9B8C3FBBDD5E7A7B667057F0D8EE8E1B
   s = 02C36A127A7B89EDBB72E4FFBC71DABC7D4FC69C
   With SHA-1, message = "test":
   k = 5C842DF4F9E344EE09F056838B42C7A17F4A6433
   r = 42AB2052FD43E123F0607F115052A67DCD9C5C77
   s = 183916B0230D45B9931491D4C6B0BD2FB4AAF088
   With SHA-224, message = "test":
   k = 4598B8EFC1A53BC8AECD58D1ABBB0C0C71E67297
   r = 6868E9964E36C1689F6037F91F28D5F2C30610F2
   s = 49CEC3ACDC83018C5BD2674ECAAD35B8CD22940F
   With SHA-256, message = "test":
   k = 5A67592E8128E03A417B0484410FB72C0B630E1A
   r = 22518C127299B0F6FDC9872B282B9E70D0790812
   s = 6837EC18F150D55DE95B5E29BE7AF5D01E4FE160
   With SHA-384, message = "test":
   k = 220156B761F6CA5E6C9F1B9CF9C24BE25F98CD89
   r = 854CF929B58D73C3CBFDC421E8D5430CD6DB5E66
   s = 91D0E0F53E22F898D158380676A871A157CDA622
   With SHA-512, message = "test":
   k = 65D2C2EEB175E370F28C75BFCDC028D22C7DBE9C
   r = 8EA47E475BA8AC6F2D821DA3BD212D11A3DEB9A0
   s = 7C670C7AD72B6C050C109E1790008097125433E8
A.2.2. DSA, 2048 Bits
A.2.2. DSA、2048ビット

Key pair:


key parameters:


   p = 9DB6FB5951B66BB6FE1E140F1D2CE5502374161FD6538DF1648218642F0B5C48
   q = F2C3119374CE76C9356990B465374A17F23F9ED35089BD969F61C6DDE9998C1F
   g = 5C7FF6B06F8F143FE8288433493E4769C4D988ACE5BE25A0E24809670716C613

private key:


   x = 69C7548C21D0DFEA6B9A51C9EAD4E27C33D3B3F180316E5BCAB92C933F0E4DBC

public key:


   y = 667098C654426C78D7F8201EAC6C203EF030D43605032C2F1FA937E5237DBD94



   With SHA-1, message = "sample":
   k = 888FA6F7738A41BDC9846466ABDB8174C0338250AE50CE955CA16230F9CBD53E
   r = 3A1B2DBD7489D6ED7E608FD036C83AF396E290DBD602408E8677DAABD6E7445A
   s = D26FCBA19FA3E3058FFC02CA1596CDBB6E0D20CB37B06054F7E36DED0CDBBCCF
   With SHA-224, message = "sample":
   k = BC372967702082E1AA4FCE892209F71AE4AD25A6DFD869334E6F153BD0C4D806
   r = DC9F4DEADA8D8FF588E98FED0AB690FFCE858DC8C79376450EB6B76C24537E2C
   s = A65A9C3BC7BABE286B195D5DA68616DA8D47FA0097F36DD19F517327DC848CEC
   With SHA-256, message = "sample":
   k = 8926A27C40484216F052F4427CFD5647338B7B3939BC6573AF4333569D597C52
   r = EACE8BDBBE353C432A795D9EC556C6D021F7A03F42C36E9BC87E4AC7932CC809
   s = 7081E175455F9247B812B74583E9E94F9EA79BD640DC962533B0680793A38D53
   With SHA-384, message = "sample":
   k = C345D5AB3DA0A5BCB7EC8F8FB7A7E96069E03B206371EF7D83E39068EC564920
   r = B2DA945E91858834FD9BF616EBAC151EDBC4B45D27D0DD4A7F6A22739F45C00B
   s = 19048B63D9FD6BCA1D9BAE3664E1BCB97F7276C306130969F63F38FA8319021B
   With SHA-512, message = "sample":
   k = 5A12994431785485B3F5F067221517791B85A597B7A9436995C89ED0374668FC
   r = 2016ED092DC5FB669B8EFB3D1F31A91EECB199879BE0CF78F02BA062CB4C942E
   s = D0C76F84B5F091E141572A639A4FB8C230807EEA7D55C8A154A224400AFF2351
   With SHA-1, message = "test":
   k = 6EEA486F9D41A037B2C640BC5645694FF8FF4B98D066A25F76BE641CCB24BA4F
   r = C18270A93CFC6063F57A4DFA86024F700D980E4CF4E2CB65A504397273D98EA0
   s = 414F22E5F31A8B6D33295C7539C1C1BA3A6160D7D68D50AC0D3A5BEAC2884FAA
   With SHA-224, message = "test":
   k = 06BD4C05ED74719106223BE33F2D95DA6B3B541DAD7BFBD7AC508213B6DA6670
   r = 272ABA31572F6CC55E30BF616B7A265312018DD325BE031BE0CC82AA17870EA3
   s = E9CC286A52CCE201586722D36D1E917EB96A4EBDB47932F9576AC645B3A60806
   With SHA-256, message = "test":
   k = 1D6CE6DDA1C5D37307839CD03AB0A5CBB18E60D800937D67DFB4479AAC8DEAD7
   r = 8190012A1969F9957D56FCCAAD223186F423398D58EF5B3CEFD5A4146A4476F0
   s = 7452A53F7075D417B4B013B278D1BB8BBD21863F5E7B1CEE679CF2188E1AB19E
   With SHA-384, message = "test":
   k = 206E61F73DBE1B2DC8BE736B22B079E9DACD974DB00EEBBC5B64CAD39CF9F91C
   r = 239E66DDBE8F8C230A3D071D601B6FFBDFB5901F94D444C6AF56F732BEB954BE
   s = 6BD737513D5E72FE85D1C750E0F73921FE299B945AAD1C802F15C26A43D34961
   With SHA-512, message = "test":
   k = AFF1651E4CD6036D57AA8B2A05CCF1A9D5A40166340ECBBDC55BE10B568AA0AA
   r = 89EC4BB1400ECCFF8E7D9AA515CD1DE7803F2DAFF09693EE7FD1353E90A68307
   s = C9F0BDABCC0D880BB137A994CC7F3980CE91CC10FAF529FC46565B15CEA854E1
A.2.3. ECDSA, 192 Bits (Prime Field)
A.2.3. ECDSA、192ビット(プライムフィールド)

Key pair:


curve: NIST P-192

曲線:NIST P-192

q = FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831 (qlen = 192 bits)

q = FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831(qlen = 192ビット)

private key:


   x = 6FAB034934E4C0FC9AE67F5B5659A9D7D1FEFD187EE09FD4

public key: U = xG

公開鍵:U = xG

   Ux = AC2C77F529F91689FEA0EA5EFEC7F210D8EEA0B9E047ED56
   Uy = 3BC723E57670BD4887EBC732C523063D0A7C957BC97C1C43



   With SHA-1, message = "sample":
   k = 37D7CA00D2C7B0E5E412AC03BD44BA837FDD5B28CD3B0021
   r = 98C6BD12B23EAF5E2A2045132086BE3EB8EBD62ABF6698FF
   s = 57A22B07DEA9530F8DE9471B1DC6624472E8E2844BC25B64
   With SHA-224, message = "sample":
   k = 4381526B3FC1E7128F202E194505592F01D5FF4C5AF015D8
   r = A1F00DAD97AEEC91C95585F36200C65F3C01812AA60378F5
   s = E07EC1304C7C6C9DEBBE980B9692668F81D4DE7922A0F97A
   With SHA-256, message = "sample":
   k = 32B1B6D7D42A05CB449065727A84804FB1A3E34D8F261496
   r = 4B0B8CE98A92866A2820E20AA6B75B56382E0F9BFD5ECB55
   s = CCDB006926EA9565CBADC840829D8C384E06DE1F1E381B85
   With SHA-384, message = "sample":
   k = 4730005C4FCB01834C063A7B6760096DBE284B8252EF4311
   r = DA63BF0B9ABCF948FBB1E9167F136145F7A20426DCC287D5
   s = C3AA2C960972BD7A2003A57E1C4C77F0578F8AE95E31EC5E
   With SHA-512, message = "sample":
   k = A2AC7AB055E4F20692D49209544C203A7D1F2C0BFBC75DB1
   r = 4D60C5AB1996BD848343B31C00850205E2EA6922DAC2E4B8
   s = 3F6E837448F027A1BF4B34E796E32A811CBB4050908D8F67
   With SHA-1, message = "test":
   k = D9CF9C3D3297D3260773A1DA7418DB5537AB8DD93DE7FA25
   r = 0F2141A0EBBC44D2E1AF90A50EBCFCE5E197B3B7D4DE036D
   s = EB18BC9E1F3D7387500CB99CF5F7C157070A8961E38700B7
   With SHA-224, message = "test":
   k = F5DC805F76EF851800700CCE82E7B98D8911B7D510059FBE
   r = 6945A1C1D1B2206B8145548F633BB61CEF04891BAF26ED34
   s = B7FB7FDFC339C0B9BD61A9F5A8EAF9BE58FC5CBA2CB15293
   With SHA-256, message = "test":
   k = 5C4CE89CF56D9E7C77C8585339B006B97B5F0680B4306C6C
   r = 3A718BD8B4926C3B52EE6BBE67EF79B18CB6EB62B1AD97AE
   s = 5662E6848A4A19B1F1AE2F72ACD4B8BBE50F1EAC65D9124F
   With SHA-384, message = "test":
   k = 5AFEFB5D3393261B828DB6C91FBC68C230727B030C975693
   r = B234B60B4DB75A733E19280A7A6034BD6B1EE88AF5332367
   s = 7994090B2D59BB782BE57E74A44C9A1C700413F8ABEFE77A
   With SHA-512, message = "test":
   k = 0758753A5254759C7CFBAD2E2D9B0792EEE44136C9480527
   r = FE4F4AE86A58B6507946715934FE2D8FF9D95B6B098FE739
   s = 74CF5605C98FBA0E1EF34D4B5A1577A7DCF59457CAE52290
A.2.4. ECDSA, 224 Bits (Prime Field)
A.2.4. ECDSA、224ビット(プライムフィールド)

Key pair:


curve: NIST P-224

曲線:NIST P-224

q = FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D (qlen = 224 bits)


private key:


   x = F220266E1105BFE3083E03EC7A3A654651F45E37167E88600BF257C1

public key: U = xG

公開鍵:U = xG

   Ux = 00CF08DA5AD719E42707FA431292DEA11244D64FC51610D94B130D6C
   Uy = EEAB6F3DEBE455E3DBF85416F7030CBD94F34F2D6F232C69F3C1385A



   With SHA-1, message = "sample":
   k = 7EEFADD91110D8DE6C2C470831387C50D3357F7F4D477054B8B426BC
   r = 22226F9D40A96E19C4A301CE5B74B115303C0F3A4FD30FC257FB57AC
   s = 66D1CDD83E3AF75605DD6E2FEFF196D30AA7ED7A2EDF7AF475403D69
   With SHA-224, message = "sample":
   k = C1D1F2F10881088301880506805FEB4825FE09ACB6816C36991AA06D
   r = 1CDFE6662DDE1E4A1EC4CDEDF6A1F5A2FB7FBD9145C12113E6ABFD3E
   s = A6694FD7718A21053F225D3F46197CA699D45006C06F871808F43EBC
   With SHA-256, message = "sample":
   k = AD3029E0278F80643DE33917CE6908C70A8FF50A411F06E41DEDFCDC
   r = 61AA3DA010E8E8406C656BC477A7A7189895E7E840CDFE8FF42307BA
   s = BC814050DAB5D23770879494F9E0A680DC1AF7161991BDE692B10101
   With SHA-384, message = "sample":
   k = 52B40F5A9D3D13040F494E83D3906C6079F29981035C7BD51E5CAC40
   r = 0B115E5E36F0F9EC81F1325A5952878D745E19D7BB3EABFABA77E953
   s = 830F34CCDFE826CCFDC81EB4129772E20E122348A2BBD889A1B1AF1D
   With SHA-512, message = "sample":
   k = 9DB103FFEDEDF9CFDBA05184F925400C1653B8501BAB89CEA0FBEC14
   r = 074BD1D979D5F32BF958DDC61E4FB4872ADCAFEB2256497CDAC30397
   s = A4CECA196C3D5A1FF31027B33185DC8EE43F288B21AB342E5D8EB084
   With SHA-1, message = "test":
   k = 2519178F82C3F0E4F87ED5883A4E114E5B7A6E374043D8EFD329C253
   r = DEAA646EC2AF2EA8AD53ED66B2E2DDAA49A12EFD8356561451F3E21C
   s = 95987796F6CF2062AB8135271DE56AE55366C045F6D9593F53787BD2
   With SHA-224, message = "test":
   k = DF8B38D40DCA3E077D0AC520BF56B6D565134D9B5F2EAE0D34900524
   r = C441CE8E261DED634E4CF84910E4C5D1D22C5CF3B732BB204DBEF019
   s = 902F42847A63BDC5F6046ADA114953120F99442D76510150F372A3F4
   With SHA-256, message = "test":
   k = FF86F57924DA248D6E44E8154EB69F0AE2AEBAEE9931D0B5A969F904
   r = AD04DDE87B84747A243A631EA47A1BA6D1FAA059149AD2440DE6FBA6
   s = 178D49B1AE90E3D8B629BE3DB5683915F4E8C99FDF6E666CF37ADCFD
   With SHA-384, message = "test":
   k = 7046742B839478C1B5BD31DB2E862AD868E1A45C863585B5F22BDC2D
   r = 389B92682E399B26518A95506B52C03BC9379A9DADF3391A21FB0EA4
   s = 414A718ED3249FF6DBC5B50C27F71F01F070944DA22AB1F78F559AAB
   With SHA-512, message = "test":
   k = E39C2AA4EA6BE2306C72126D40ED77BF9739BB4D6EF2BBB1DCB6169D
   r = 049F050477C5ADD858CAC56208394B5A55BAEBBE887FDF765047C17C
   s = 077EB13E7005929CEFA3CD0403C7CDCC077ADF4E44F3C41B2F60ECFF
A.2.5. ECDSA, 256 Bits (Prime Field)
A.2.5. ECDSA、256ビット(Prime Field)

Key pair:


curve: NIST P-256

曲線:NIST P-256

q = FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551 (qlen = 256 bits)

q = FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551(qlen = 256ビット)

private key:


   x = C9AFA9D845BA75166B5C215767B1D6934E50C3DB36E89B127B8A622B120F6721

public key: U = xG

公開鍵:U = xG

   Ux = 60FED4BA255A9D31C961EB74C6356D68C049B8923B61FA6CE669622E60F29FB6
   Uy = 7903FE1008B8BC99A41AE9E95628BC64F2F1B20C2D7E9F5177A3C294D4462299



   With SHA-1, message = "sample":
   k = 882905F1227FD620FBF2ABF21244F0BA83D0DC3A9103DBBEE43A1FB858109DB4
   r = 61340C88C3AAEBEB4F6D667F672CA9759A6CCAA9FA8811313039EE4A35471D32
   s = 6D7F147DAC089441BB2E2FE8F7A3FA264B9C475098FDCF6E00D7C996E1B8B7EB
   With SHA-224, message = "sample":
   k = 103F90EE9DC52E5E7FB5132B7033C63066D194321491862059967C715985D473
   r = 53B2FFF5D1752B2C689DF257C04C40A587FABABB3F6FC2702F1343AF7CA9AA3F
   s = B9AFB64FDC03DC1A131C7D2386D11E349F070AA432A4ACC918BEA988BF75C74C
   With SHA-256, message = "sample":
   k = A6E3C57DD01ABE90086538398355DD4C3B17AA873382B0F24D6129493D8AAD60
   r = EFD48B2AACB6A8FD1140DD9CD45E81D69D2C877B56AAF991C34D0EA84EAF3716
   s = F7CB1C942D657C41D436C7A1B6E29F65F3E900DBB9AFF4064DC4AB2F843ACDA8
   With SHA-384, message = "sample":
   k = 09F634B188CEFD98E7EC88B1AA9852D734D0BC272F7D2A47DECC6EBEB375AAD4
   r = 0EAFEA039B20E9B42309FB1D89E213057CBF973DC0CFC8F129EDDDC800EF7719
   s = 4861F0491E6998B9455193E34E7B0D284DDD7149A74B95B9261F13ABDE940954
   With SHA-512, message = "sample":
   k = 5FA81C63109BADB88C1F367B47DA606DA28CAD69AA22C4FE6AD7DF73A7173AA5
   r = 8496A60B5E9B47C825488827E0495B0E3FA109EC4568FD3F8D1097678EB97F00
   s = 2362AB1ADBE2B8ADF9CB9EDAB740EA6049C028114F2460F96554F61FAE3302FE
   With SHA-1, message = "test":
   k = 8C9520267C55D6B980DF741E56B4ADEE114D84FBFA2E62137954164028632A2E
   r = 0CBCC86FD6ABD1D99E703E1EC50069EE5C0B4BA4B9AC60E409E8EC5910D81A89
   s = 01B9D7B73DFAA60D5651EC4591A0136F87653E0FD780C3B1BC872FFDEAE479B1
   With SHA-224, message = "test":
   k = 669F4426F2688B8BE0DB3A6BD1989BDAEFFF84B649EEB84F3DD26080F667FAA7
   r = C37EDB6F0AE79D47C3C27E962FA269BB4F441770357E114EE511F662EC34A692
   s = C820053A05791E521FCAAD6042D40AEA1D6B1A540138558F47D0719800E18F2D
   With SHA-256, message = "test":
   k = D16B6AE827F17175E040871A1C7EC3500192C4C92677336EC2537ACAEE0008E0
   r = F1ABB023518351CD71D881567B1EA663ED3EFCF6C5132B354F28D3B0B7D38367
   s = 019F4113742A2B14BD25926B49C649155F267E60D3814B4C0CC84250E46F0083
   With SHA-384, message = "test":
   k = 16AEFFA357260B04B1DD199693960740066C1A8F3E8EDD79070AA914D361B3B8
   r = 83910E8B48BB0C74244EBDF7F07A1C5413D61472BD941EF3920E623FBCCEBEB6
   s = 8DDBEC54CF8CD5874883841D712142A56A8D0F218F5003CB0296B6B509619F2C
   With SHA-512, message = "test":
   k = 6915D11632ACA3C40D5D51C08DAF9C555933819548784480E93499000D9F0B7F
   r = 461D93F31B6540894788FD206C07CFA0CC35F46FA3C91816FFF1040AD1581A04
   s = 39AF9F15DE0DB8D97E72719C74820D304CE5226E32DEDAE67519E840D1194E55
A.2.6. ECDSA, 384 Bits (Prime Field)
A.2.6. ECDSA、384ビット(プライムフィールド)

Key pair:


curve: NIST P-384

曲線:NIST P-384



private key:


   x = 6B9D3DAD2E1B8C1C05B19875B6659F4DE23C3B667BF297BA9AA47740787137D8

public key: U = xG

公開鍵:U = xG

   Ux = EC3A4E415B4E19A4568618029F427FA5DA9A8BC4AE92E02E06AAE5286B300C64
   Uy = 8015D9B72D7D57244EA8EF9AC0C621896708A59367F9DFB9F54CA84B3F1C9DB1



   With SHA-1, message = "sample":
   k = 4471EF7518BB2C7C20F62EAE1C387AD0C5E8E470995DB4ACF694466E6AB09663
   r = EC748D839243D6FBEF4FC5C4859A7DFFD7F3ABDDF72014540C16D73309834FA3
   s = A3BCFA947BEEF4732BF247AC17F71676CB31A847B9FF0CBC9C9ED4C1A5B3FACF
   With SHA-224, message = "sample":
   k = A4E4D2F0E729EB786B31FC20AD5D849E304450E0AE8E3E341134A5C1AFA03CAB
   r = 42356E76B55A6D9B4631C865445DBE54E056D3B3431766D0509244793C3F9366
   s = 9DA0C81787064021E78DF658F2FBB0B042BF304665DB721F077A4298B095E483
   With SHA-256, message = "sample":
   k = 180AE9F9AEC5438A44BC159A1FCB277C7BE54FA20E7CF404B490650A8ACC414E
   r = 21B13D1E013C7FA1392D03C5F99AF8B30C570C6F98D4EA8E354B63A21D3DAA33
   s = F3AA443FB107745BF4BD77CB3891674632068A10CA67E3D45DB2266FA7D1FEEB
   With SHA-384, message = "sample":
   k = 94ED910D1A099DAD3254E9242AE85ABDE4BA15168EAF0CA87A555FD56D10FBCA
   r = 94EDBB92A5ECB8AAD4736E56C691916B3F88140666CE9FA73D64C4EA95AD133C
   s = 99EF4AEB15F178CEA1FE40DB2603138F130E740A19624526203B6351D0A3A94F
   With SHA-512, message = "sample":
   k = 92FC3C7183A883E24216D1141F1A8976C5B0DD797DFA597E3D7B32198BD35331
   r = ED0959D5880AB2D869AE7F6C2915C6D60F96507F9CB3E047C0046861DA4A799C
   s = 512C8CCEEE3890A84058CE1E22DBC2198F42323CE8ACA9135329F03C068E5112
   With SHA-1, message = "test":
   k = 66CC2C8F4D303FC962E5FF6A27BD79F84EC812DDAE58CF5243B64A4AD8094D47
   r = 4BC35D3A50EF4E30576F58CD96CE6BF638025EE624004A1F7789A8B8E43D0678
   s = D5A6326C494ED3FF614703878961C0FDE7B2C278F9A65FD8C4B7186201A29916
   With SHA-224, message = "test":
   k = 18FA39DB95AA5F561F30FA3591DC59C0FA3653A80DAFFA0B48D1A4C6DFCBFF6E
   r = E8C9D0B6EA72A0E7837FEA1D14A1A9557F29FAA45D3E7EE888FC5BF954B5E624
   s = 07041D4A7A0379AC7232FF72E6F77B6DDB8F09B16CCE0EC3286B2BD43FA8C614
   With SHA-256, message = "test":
   k = 0CFAC37587532347DC3389FDC98286BBA8C73807285B184C83E62E26C401C0FA
   r = 6D6DEFAC9AB64DABAFE36C6BF510352A4CC27001263638E5B16D9BB51D451559
   s = 2D46F3BECBCC523D5F1A1256BF0C9B024D879BA9E838144C8BA6BAEB4B53B47D
   With SHA-384, message = "test":
   k = 015EE46A5BF88773ED9123A5AB0807962D193719503C527B031B4C2D225092AD
   r = 8203B63D3C853E8D77227FB377BCF7B7B772E97892A80F36AB775D509D7A5FEB
   s = DDD0760448D42D8A43AF45AF836FCE4DE8BE06B485E9B61B827C2F13173923E0
   With SHA-512, message = "test":
   k = 3780C4F67CB15518B6ACAE34C9F83568D2E12E47DEAB6C50A4E4EE5319D1E8CE
   r = A0D5D090C9980FAF3C2CE57B7AE951D31977DD11C775D314AF55F76C676447D0
   s = 976984E59B4C77B0E8E4460DCA3D9F20E07B9BB1F63BEEFAF576F6B2E8B22463
A.2.7. ECDSA, 521 Bits (Prime Field)
A.2.7. ECDSA、521ビット(プライムフィールド)

Key pair:


curve: NIST P-521

曲線:NIST P-521



private key:


x = 0FAD06DAA62BA3B25D2FB40133DA757205DE67F5BB0018FEE8C86E1B68C7E75C AA896EB32F1F47C70855836A6D16FCC1466F6D8FBEC67DB89EC0C08B0E996B83 538

x = 0FAD06DAA62BA3B25D2FB40133DA757205DE67F5BB0018FEE8C86E1B68C7E75C AA896EB32F1F47C70855836A6D16FCC1466F6D8FBEC67DB89EC0C08B0E996B83 538

public key: U = xG

公開鍵:U = xG

Ux = 1894550D0785932E00EAA23B694F213F8C3121F86DC97A04E5A7167DB4E5BCD3 71123D46E45DB6B5D5370A7F20FB633155D38FFA16D2BD761DCAC474B9A2F502 3A4

Ux = 1894550D0785932E00EAA23B694F213F8C3121F8​​6DC97A04E5A7167DB4E5BCD3 71123D46E45DB6B5D5370A7F20FB633155D38FFA16D2BD761DCAC474B9A2F502 3A4

Uy = 0493101C962CD4D2FDDF782285E64584139C2F91B47F87FF82354D6630F746A2 8A0DB25741B5B34A828008B22ACC23F924FAAFBD4D33F81EA66956DFEAA2BFDF CF5

Uy = 0493101C962CD4D2FDDF782285E64584139C2F91B47F87FF82354D6630F746A2 8A0DB25741B5B34A828008B22ACC23F924FAAFBD4D33F81EA66956DFEAA2BFDF CF5



With SHA-1, message = "sample": k = 089C071B419E1C2820962321787258469511958E80582E95D8378E0C2CCDB3CB 42BEDE42F50E3FA3C71F5A76724281D31D9C89F0F91FC1BE4918DB1C03A5838D 0F9 r = 0343B6EC45728975EA5CBA6659BBB6062A5FF89EEA58BE3C80B619F322C87910 FE092F7D45BB0F8EEE01ED3F20BABEC079D202AE677B243AB40B5431D497C55D 75D s = 0E7B0E675A9B24413D448B8CC119D2BF7B2D2DF032741C096634D6D65D0DBE3D 5694625FB9E8104D3B842C1B0E2D0B98BEA19341E8676AEF66AE4EBA3D5475D5 D16

K = 089C071B419E1C2820962321787258469511958E80582E95D8378E0C2CCDB3CB 42BEDE42F50E3FA3C71F5A76724281D31D9C89F0F91FC1BE4918DB1C03A5838D 0F9 R = 0343B6EC45728975EA5CBA6659BBB6062A5FF89EEA58BE3C80B619F322C87910 FE092F7D45BB0F8EEE01ED3F20BABEC079D202AE677B243AB40B5431D497C55D 75D S = 0E7B0E675A9B24413D448B8CC119D2BF7B2D2DF032741C096634D6D65D0DBE3D 5694625FB9E8104D3B842C1B0E2D0B98BEA19341E8676AEF66AE4EBA3D5475D5 D16:SHA-1、メッセージ= "サンプル" と

With SHA-224, message = "sample": k = 121415EC2CD7726330A61F7F3FA5DE14BE9436019C4DB8CB4041F3B54CF31BE0 493EE3F427FB906393D895A19C9523F3A1D54BB8702BD4AA9C99DAB2597B9211 3F3 r = 1776331CFCDF927D666E032E00CF776187BC9FDD8E69D0DABB4109FFE1B5E2A3 0715F4CC923A4A5E94D2503E9ACFED92857B7F31D7152E0F8C00C15FF3D87E2E D2E s = 050CB5265417FE2320BBB5A122B8E1A32BD699089851128E360E620A30C7E17B A41A666AF126CE100E5799B153B60528D5300D08489CA9178FB610A2006C254B 41F

SHA-224と、メッセージ= "サンプル":K = 121415EC2CD7726330A61F7F3FA5DE14BE9436019C4DB8CB4041F3B54CF31BE0 493EE3F427FB906393D895A19C9523F3A1D54BB8702BD4AA9C99DAB2597B9211 3F3 R = 1776331CFCDF927D666E032E00CF776187BC9FDD8E69D0DABB4109FFE1B5E2A3 0715F4CC923A4A5E94D2503E9ACFED92857B7F31D7152E0F8C00C15FF3D87E2E D2E S = 050CB5265417FE2320BBB5A122B8E1A32BD699089851128E360E620A30C7E17B A41A666AF126CE100E5799B153B60528D5300D08489CA9178FB610A2006C254B 41F

With SHA-256, message = "sample": k = 0EDF38AFCAAECAB4383358B34D67C9F2216C8382AAEA44A3DAD5FDC9C3257576 1793FEF24EB0FC276DFC4F6E3EC476752F043CF01415387470BCBD8678ED2C7E 1A0 r = 1511BB4D675114FE266FC4372B87682BAECC01D3CC62CF2303C92B3526012659 D16876E25C7C1E57648F23B73564D67F61C6F14D527D54972810421E7D87589E 1A7 s = 04A171143A83163D6DF460AAF61522695F207A58B95C0644D87E52AA1A347916 E4F7A72930B1BC06DBE22CE3F58264AFD23704CBB63B29B931F7DE6C9D949A7E CFC

K = 0EDF38AFCAAECAB4383358B34D67C9F2216C8382AAEA44A3DAD5FDC9C3257576 1793FEF24EB0FC276DFC4F6E3EC476752F043CF01415387470BCBD8678ED2C7E 1A0 R = 1511BB4D675114FE266FC4372B87682BAECC01D3CC62CF2303C92B3526012659 D16876E25C7C1E57648F23B73564D67F61C6F14D527D54972810421E7D87589E 1A7 S = 04A171143A83163D6DF460AAF61522695F207A58B95C0644D87E52AA1A347916 E4F7A72930B1BC06DBE22CE3F58264AFD23704CBB63B29B931F7DE6C9D949A7E CFC:SHA-256、メッセージ= "サンプル" と

With SHA-384, message = "sample": k = 1546A108BC23A15D6F21872F7DED661FA8431DDBD922D0DCDB77CC878C8553FF AD064C95A920A750AC9137E527390D2D92F153E66196966EA554D9ADFCB109C4 211 r = 1EA842A0E17D2DE4F92C15315C63DDF72685C18195C2BB95E572B9C5136CA4B4 B576AD712A52BE9730627D16054BA40CC0B8D3FF035B12AE75168397F5D50C67 451 s = 1F21A3CEE066E1961025FB048BD5FE2B7924D0CD797BABE0A83B66F1E35EEAF5 FDE143FA85DC394A7DEE766523393784484BDF3E00114A1C857CDE1AA203DB65 D61

SHA-384と、メッセージ= "サンプル":K = 1546A108BC23A15D6F21872F7DED661FA8431DDBD922D0DCDB77CC878C8553FF AD064C95A920A750AC9137E527390D2D92F153E66196966EA554D9ADFCB109C4 211 R = 1EA842A0E17D2DE4F92C15315C63DDF72685C18195C2BB95E572B9C5136CA4B4 B576AD712A52BE9730627D16054BA40CC0B8D3FF035B12AE75168397F5D50C67 451 S = 1F21A3CEE066E1961025FB048BD5FE2B7924D0CD797BABE0A83B66F1E35EEAF5 FDE143FA85DC394A7DEE766523393784484BDF3E00114A1C857CDE1AA203DB65 D61

With SHA-512, message = "sample": k = 1DAE2EA071F8110DC26882D4D5EAE0621A3256FC8847FB9022E2B7D28E6F1019 8B1574FDD03A9053C08A1854A168AA5A57470EC97DD5CE090124EF52A2F7ECBF FD3 r = 0C328FAFCBD79DD77850370C46325D987CB525569FB63C5D3BC53950E6D4C5F1 74E25A1EE9017B5D450606ADD152B534931D7D4E8455CC91F9B15BF05EC36E37 7FA s = 0617CCE7CF5064806C467F678D3B4080D6F1CC50AF26CA209417308281B68AF2 82623EAA63E5B5C0723D8B8C37FF0777B1A20F8CCB1DCCC43997F1EE0E44DA4A 67A

K = 1DAE2EA071F8110DC26882D4D5EAE0621A3256FC8847FB9022E2B7D28E6F1019 8B1574FDD03A9053C08A1854A168AA5A57470EC97DD5CE090124EF52A2F7ECBF FD3のR = 0C328FAFCBD79DD77850370C46325D987CB525569FB63C5D3BC53950E6D4C5F1 74E25A1EE9017B5D450606ADD152B534931D7D4E8455CC91F9B15BF05EC36E37 7FA S = 0617CCE7CF5064806C467F678D3B4080D6F1CC50AF26CA209417308281B68AF2 82623EAA63E5B5C0723D8B8C37FF0777B1A20F8CCB1DCCC43997F1EE0E44DA4A 67A:SHA-512、メッセージ= "サンプル" と

With SHA-1, message = "test": k = 0BB9F2BF4FE1038CCF4DABD7139A56F6FD8BB1386561BD3C6A4FC818B20DF5DD BA80795A947107A1AB9D12DAA615B1ADE4F7A9DC05E8E6311150F47F5C57CE8B 222 r = 13BAD9F29ABE20DE37EBEB823C252CA0F63361284015A3BF430A46AAA80B87B0 693F0694BD88AFE4E661FC33B094CD3B7963BED5A727ED8BD6A3A202ABE009D0 367 s = 1E9BB81FF7944CA409AD138DBBEE228E1AFCC0C890FC78EC8604639CB0DBDC90 F717A99EAD9D272855D00162EE9527567DD6A92CBD629805C0445282BBC91679 7FF

SHA-1と、メッセージ= "テスト" K = 0BB9F2BF4FE1038CCF4DABD7139A56F6FD8BB1386561BD3C6A4FC818B20DF5DD BA80795A947107A1AB9D12DAA615B1ADE4F7A9DC05E8E6311150F47F5C57CE8B 222 R = 13BAD9F29ABE20DE37EBEB823C252CA0F63361284015A3BF430A46AAA80B87B0 693F0694BD88AFE4E661FC33B094CD3B7963BED5A727ED8BD6A3A202ABE009D0 367 S = 1E9BB81FF7944CA409AD138DBBEE228E1AFCC0C890FC78EC8604639CB0DBDC90 F717A99EAD9D272855D00162EE9527567DD6A92CBD629805C0445282BBC91679 7FF

With SHA-224, message = "test": k = 040D09FCF3C8A5F62CF4FB223CBBB2B9937F6B0577C27020A99602C25A011369 87E452988781484EDBBCF1C47E554E7FC901BC3085E5206D9F619CFF07E73D6F 706 r = 1C7ED902E123E6815546065A2C4AF977B22AA8EADDB68B2C1110E7EA44D42086 BFE4A34B67DDC0E17E96536E358219B23A706C6A6E16BA77B65E1C595D43CAE1 7FB s = 177336676304FCB343CE028B38E7B4FBA76C1C1B277DA18CAD2A8478B2A9A9F5 BEC0F3BA04F35DB3E4263569EC6AADE8C92746E4C82F8299AE1B8F1739F8FD51 9A4

K = 040D09FCF3C8A5F62CF4FB223CBBB2B9937F6B0577C27020A99602C25A011369 87E452988781484EDBBCF1C47E554E7FC901BC3085E5206D9F619CFF07E73D6F 706 R = 1C7ED902E123E6815546065A2C4AF977B22AA8EADDB68B2C1110E7EA44D42086 BFE4A34B67DDC0E17E96536E358219B23A706C6A6E16BA77B65E1C595D43CAE1 7FB S = 177336676304FCB343CE028B38E7B4FBA76C1C1B277DA18CAD2A8478B2A9A9F5 BEC0F3BA04F35DB3E4263569EC6AADE8C92746E4C82F8299AE1B8F1739F8FD51 9A4:SHA-224、メッセージ= "テスト" と

With SHA-256, message = "test": k = 01DE74955EFAABC4C4F17F8E84D881D1310B5392D7700275F82F145C61E84384 1AF09035BF7A6210F5A431A6A9E81C9323354A9E69135D44EBD2FCAA7731B909 258 r = 00E871C4A14F993C6C7369501900C4BC1E9C7B0B4BA44E04868B30B41D807104 2EB28C4C250411D0CE08CD197E4188EA4876F279F90B3D8D74A3C76E6F1E4656 AA8 s = 0CD52DBAA33B063C3A6CD8058A1FB0A46A4754B034FCC644766CA14DA8CA5CA9 FDE00E88C1AD60CCBA759025299079D7A427EC3CC5B619BFBC828E7769BCD694 E86

SHA-256、メッセージ= "テスト" K = 01DE74955EFAABC4C4F17F8E84D881D1310B5392D7700275F82F145C61E84384 1AF09035BF7A6210F5A431A6A9E81C9323354A9E69135D44EBD2FCAA7731B909 258 R = 00E871C4A14F993C6C7369501900C4BC1E9C7B0B4BA44E04868B30B41D807104 2EB28C4C250411D0CE08CD197E4188EA4876F279F90B3D8D74A3C76E6F1E4656 AA8 S = 0CD52DBAA33B063C3A6CD8058A1FB0A46A4754B034FCC644766CA14DA8CA5CA9 FDE00E88C1AD60CCBA759025299079D7A427EC3CC5B619BFBC828E7769BCD694 E86

With SHA-384, message = "test": k = 1F1FC4A349A7DA9A9E116BFDD055DC08E78252FF8E23AC276AC88B1770AE0B5D CEB1ED14A4916B769A523CE1E90BA22846AF11DF8B300C38818F713DADD85DE0 C88 r = 14BEE21A18B6D8B3C93FAB08D43E739707953244FDBE924FA926D76669E7AC8C 89DF62ED8975C2D8397A65A49DCC09F6B0AC62272741924D479354D74FF60755 78C s = 133330865C067A0EAF72362A65E2D7BC4E461E8C8995C3B6226A21BD1AA78F0E D94FE536A0DCA35534F0CD1510C41525D163FE9D74D134881E35141ED5E8E95B 979

SHA-384と、メッセージ= "テスト" K = 1F1FC4A349A7DA9A9E116BFDD055DC08E78252FF8E23AC276AC88B1770AE0B5D CEB1ED14A4916B769A523CE1E90BA22846AF11DF8B300C38818F713DADD85DE0 C88 R = 14BEE21A18B6D8B3C93FAB08D43E739707953244FDBE924FA926D76669E7AC8C 89DF62ED8975C2D8397A65A49DCC09F6B0AC62272741924D479354D74FF60755 78C S = 133330865C067A0EAF72362A65E2D7BC4E461E8C8995C3B6226A21BD1AA78F0E D94FE536A0DCA35534F0CD1510C41525D163FE9D74D134881E35141ED5E8E95B 979

With SHA-512, message = "test": k = 16200813020EC986863BEDFC1B121F605C1215645018AEA1A7B215A564DE9EB1 B38A67AA1128B80CE391C4FB71187654AAA3431027BFC7F395766CA988C964DC 56D r = 13E99020ABF5CEE7525D16B69B229652AB6BDF2AFFCAEF38773B4B7D08725F10 CDB93482FDCC54EDCEE91ECA4166B2A7C6265EF0CE2BD7051B7CEF945BABD47E E6D s = 1FBD0013C674AA79CB39849527916CE301C66EA7CE8B80682786AD60F98F7E78 A19CA69EFF5C57400E3B3A0AD66CE0978214D13BAF4E9AC60752F7B155E2DE4D CE3

K = 16200813020EC986863BEDFC1B121F605C1215645018AEA1A7B215A564DE9EB1 B38A67AA1128B80CE391C4FB71187654AAA3431027BFC7F395766CA988C964DC 56D R = 13E99020ABF5CEE7525D16B69B229652AB6BDF2AFFCAEF38773B4B7D08725F10 CDB93482FDCC54EDCEE91ECA4166B2A7C6265EF0CE2BD7051B7CEF945BABD47E E6D S = 1FBD0013C674AA79CB39849527916CE301C66EA7CE8B80682786AD60F98F7E78 A19CA69EFF5C57400E3B3A0AD66CE0978214D13BAF4E9AC60752F7B155E2DE4D CE3:SHA-512、メッセージ= "テスト" と

A.2.8. ECDSA, 163 Bits (Binary Field, Koblitz Curve)
A.2.8. ECDSA、163ビット(バイナリフィールド、コブリッツ曲線)

Key pair:


curve: NIST K-163

曲線:NIST K-163

q = 4000000000000000000020108A2E0CC0D99F8A5EF (qlen = 163 bits)

q = 4000000000000000000020108A2E0CC0D99F8A5EF(qlen = 163ビット)

private key:


   x = 09A4D6792295A7F730FC3F2B49CBC0F62E862272F

public key: U = xG

公開鍵:U = xG

   Ux = 79AEE090DB05EC252D5CB4452F356BE198A4FF96F
   Uy = 782E29634DDC9A31EF40386E896BAA18B53AFA5A3



   With SHA-1, message = "sample":
   k = 09744429FA741D12DE2BE8316E35E84DB9E5DF1CD
   r = 30C45B80BA0E1406C4EFBBB7000D6DE4FA465D505
   s = 38D87DF89493522FC4CD7DE1553BD9DBBA2123011
   With SHA-224, message = "sample":
   k = 323E7B28BFD64E6082F5B12110AA87BC0D6A6E159
   r = 38A2749F7EA13BD5DA0C76C842F512D5A65FFAF32
   s = 064F841F70112B793FD773F5606BFA5AC2A04C1E8
   With SHA-256, message = "sample":
   k = 23AF4074C90A02B3FE61D286D5C87F425E6BDD81B
   r = 113A63990598A3828C407C0F4D2438D990DF99A7F
   s = 1313A2E03F5412DDB296A22E2C455335545672D9F
   With SHA-384, message = "sample":
   k = 2132ABE0ED518487D3E4FA7FD24F8BED1F29CCFCE
   r = 34D4DE955871BB84FEA4E7D068BA5E9A11BD8B6C4
   s = 2BAAF4D4FD57F175C405A2F39F9755D9045C820BD
   With SHA-512, message = "sample":
   k = 00BBCC2F39939388FDFE841892537EC7B1FF33AA3
   r = 38E487F218D696A7323B891F0CCF055D895B77ADC
   s = 0972D7721093F9B3835A5EB7F0442FA8DCAA873C4
   With SHA-1, message = "test":
   k = 14CAB9192F39C8A0EA8E81B4B87574228C99CD681
   r = 1375BEF93F21582F601497036A7DC8014A99C2B79
   s = 254B7F1472FFFEE9002D081BB8CE819CCE6E687F9
   With SHA-224, message = "test":
   k = 091DD986F38EB936BE053DD6ACE3419D2642ADE8D
   r = 110F17EF209957214E35E8C2E83CBE73B3BFDEE2C
   s = 057D5022392D359851B95DEC2444012502A5349CB
   With SHA-256, message = "test":
   k = 193649CE51F0CFF0784CFC47628F4FA854A93F7A2
   r = 0354D5CD24F9C41F85D02E856FA2B0001C83AF53E
   s = 020B200677731CD4FE48612A92F72A19853A82B65
   With SHA-384, message = "test":
   k = 37C73C6F8B404EC83DA17A6EBCA724B3FF1F7EEBA
   r = 11B6A84206515495AD8DBB2E5785D6D018D75817E
   s = 1A7D4C1E17D4030A5D748ADEA785C77A54581F6D0
   With SHA-512, message = "test":
   k = 331AD98D3186F73967B1E0B120C80B1E22EFC2988
   r = 148934745B351F6367FF5BB56B1848A2F508902A9
   s = 36214B19444FAB504DBA61D4D6FF2D2F9640F4837
A.2.9. ECDSA, 233 Bits (Binary Field, Koblitz Curve)
A.2.9. ECDSA、233ビット(バイナリフィールド、コブリッツ曲線)

Key pair:


curve: NIST K-233

曲線:NIST K-233

q = 8000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF (qlen = 232 bits)

q = 8000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF(qlen = 232ビット)

private key:


   x = 103B2142BDC2A3C3B55080D09DF1808F79336DA2399F5CA7171D1BE9B0

public key: U = xG

公開鍵:U = xG

   Ux = 0682886F36C68473C1A221720C2B12B9BE13458BA907E1C4736595779F2
   Uy = 1B20639B41BE0927090999B7817A3B3928D20503A39546044EC13A10309



   With SHA-1, message = "sample":
   k = 273179E3E12C69591AD3DD9C7CCE3985820E3913AB6696EB14486DDBCF
   r = 5474541C988A9A1F73899F55EF28963DFFBBF0C2B1A1EE787C6A76C6A4
   s = 46301F9EC6624257BFC70D72186F17898EDBD0A3522560A88DD1B7D45A
   With SHA-224, message = "sample":
   k = 71626A309D9CD80AD0B975D757FE6BF4B84E49F8F34C780070D7746F19
   r = 667F2FCE3E1C497EBD8E4B7C6372A8234003FE4ED6D4515814E7E11430
   s = 6A1C41340DAA730320DB9475F10E29A127D7AE3432F155E1F7954E1B57
   With SHA-256, message = "sample":
   k = 73552F9CAC5774F74F485FA253871F2109A0C86040552EAA67DBA92DC9
   r = 38AD9C1D2CB29906E7D63C24601AC55736B438FB14F4093D6C32F63A10
   s = 647AAD2599C21B6EE89BE7FF957D98F684B7921DE1FD3CC82C079624F4
   With SHA-384, message = "sample":
   k = 17D726A67539C609BD99E29AA3737EF247724B71455C3B6310034038C8
   r = 0C6510F57559C36FBCFF8C7BA4B81853DC618AD0BAAB03CFFDF3FD09FD
   s = 0AD331EE1C9B91A88BA77997235769C60AD07EE69E11F7137E17C5CF67
   With SHA-512, message = "sample":
   k = 0E535C328774CDE546BE3AF5D7FCD263872F107E807435105BA2FDC166
   r = 47C4AC1B344028CC740BA7BB9F8AA59D6390E3158153D4F2ADE4B74950
   s = 26CE0CDE18A1B884B3EE1A879C13B42F11BB7C85F7A3745C8BECEC8E6E
   With SHA-1, message = "test":
   k = 1D8BBF5CB6EFFA270A1CDC22C81E269F0CC16E27151E0A460BA9B51AFF
   r = 4780B2DE4BAA5613872179AD90664249842E8B96FCD5653B55DD63EED4
   s = 6AF46BA322E21D4A88DAEC1650EF38774231276266D6A45ED6A64ECB44
   With SHA-224, message = "test":
   k = 67634D0ABA2C9BF7AE54846F26DCD166E7100654BCE6FDC96667631AA2
   r = 61D9CC8C842DF19B3D9F4BDA0D0E14A957357ADABC239444610FB39AEA
   s = 66432278891CB594BA8D08A0C556053D15917E53449E03C2EF88474CF6
   With SHA-256, message = "test":
   k = 2CE5AEDC155ACC0DDC5E679EBACFD21308362E5EFC05C5E99B2557A8D7
   r = 05E4E6B4DB0E13034E7F1F2E5DBAB766D37C15AE4056C7EE607C8AC7F4
   s = 5FC46AA489BF828B34FBAD25EC432190F161BEA8F60D3FCADB0EE3B725
   With SHA-384, message = "test":
   k = 1B4BD3903E74FD0B31E23F956C70062014DFEFEE21832032EA5352A055
   r = 50F1EFEDFFEC1088024620280EE0D7641542E4D4B5D61DB32358FC571B
   s = 4614EAE449927A9EB2FCC42EA3E955B43D194087719511A007EC9217A5
   With SHA-512, message = "test":
   k = 1775ED919CA491B5B014C5D5E86AF53578B5A7976378F192AF665CB705
   r = 6FE6D0D3A953BB66BB01BC6B9EDFAD9F35E88277E5768D1B214395320F
   s = 7C01A236E4BFF0A771050AD01EC1D24025D3130BBD9E4E81978EB3EC09
A.2.10. ECDSA, 283 Bits (Binary Field, Koblitz Curve)
A.2.10. ECDSA、283ビット(バイナリフィールド、コブリッツ曲線)

Key pair:


curve: NIST K-283

曲線:NIST K-283

q = 1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061 E163C61 (qlen = 281 bits)


private key:


x = 06A0777356E87B89BA1ED3A3D845357BE332173C8F7A65BDC7DB4FAB3C4CC79A CC8194E

x = 06A0777356E87B89BA1ED3A3D845357BE332173C8F7A65BDC7DB4FAB3C4CC79A CC8194E

public key: U = xG

公開鍵:U = xG

Ux = 25330D0A651D5A20DC6389BC02345117725640AEC3C126612CE444EDD19649BD ECC03D6

Ux = 25330D0A651D5A20DC6389BC02345117725640AEC3C126612CE444EDD19649BD ECC03D6

Uy = 505BD60A4B67182474EC4D1C668A73140F70504A68F39EFCD972487E9530E050 8A76193

Uy = 505BD60A4B67182474EC4D1C668A73140F70504A68F39EFCD972487E9530E050 8A76193



With SHA-1, message = "sample": k = 0A96F788DECAF6C9DBE24DC75ABA6EAAE85E7AB003C8D4F83CB1540625B2993B F445692 r = 1B66D1E33FBDB6E107A69B610995C93C744CEBAEAF623CB42737C27D60188BD1 D045A68 s = 02E45B62C9C258643532FD536594B46C63B063946494F95DAFF8759FD5525023 24295C5

SHA-1を使用した場合、メッセージ= "sample":k = 0A96F788DECAF6C9DBE24DC75ABA6EAAE85E7AB003C8D4F83CB1540625B2993B F445692 r = 1B66D1E33FBDB6E107A69B610995C93C744CEBAEA462459B46B46B63B64B63B6363BB63B6363BB63B63B63B63B63B6363B64C63B64B63B63B63B64B63B63B64C63B64B63B64B63B64B63B64B63B63B64B63B64C63B64B63B64C63A64C63B64B63B64B63B63B63B64C63B64C63B64C63B64B63B64C63B64C63B64C63B64C63B64C63B64C63B64C63B64C64C64B64C64B64C64B64C64B64B64C6D64E64B64B64E64E64B64B64E64E64E64E64E64〜断念された

With SHA-224, message = "sample": k = 1B4C4E3B2F6B08B5991BD2BDDE277A7016DA527AD0AAE5BC61B64C5A0EE63E8B 502EF61 r = 018CF2F371BE86BB62E02B27CDE56DDAC83CCFBB3141FC59AEE022B66AC1A60D BBD8B76 s = 1854E02A381295EA7F184CEE71AB7222D6974522D3B99B309B1A8025EB84118A 28BF20E

SHA-224と、メッセージ= "サンプル":K = 1B4C4E3B2F6B08B5991BD2BDDE277A7016DA527AD0AAE5BC61B64C5A0EE63E8B 502EF61 R = 018CF2F371BE86BB62E02B27CDE56DDAC83CCFBB3141FC59AEE022B66AC1A60D BBD8B76 S = 1854E02A381295EA7F184CEE71AB7222D6974522D3B99B309B1A8025EB84118A 28BF20E

With SHA-256, message = "sample": k = 1CEB9E8E0DFF53CE687DEB81339ACA3C98E7A657D5A9499EF779F887A934408E CBE5A38 r = 19E90AA3DE5FB20AED22879F92C6FED278D9C9B9293CC5E94922CD952C9DBF20 DF1753A s = 135AA7443B6A25D11BB64AC482E04D47902D017752882BD72527114F46CF8BB5 6C5A8C3

SHA-256、メッセージ= "サンプル":K = 1CEB9E8E0DFF53CE687DEB81339ACA3C98E7A657D5A9499EF779F887A934408E CBE5A38 R = 19E90AA3DE5FB20AED22879F92C6FED278D9C9B9293CC5E94922CD952C9DBF20 DF1753A S = 135AA7443B6A25D11BB64AC482E04D47902D017752882BD72527114F46CF8BB5 6C5A8C3

With SHA-384, message = "sample": k = 1460A5C41745A5763A9D548AE62F2C3630BBED71B6AA549D7F829C22442A728C 5D965DA r = 0F8C1CA9C221AD9907A136F787D33BA56B0495A40E86E671C940FD767EDD75EB 6001A49 s = 1071A56915DEE89E22E511975AA09D00CDC4AA7F5054CBE83F5977EE6F8E1CC3 1EC43FD

K = 1460A5C41745A5763A9D548AE62F2C3630BBED71B6AA549D7F829C22442A728C 5D965DA R = 0F8C1CA9C221AD9907A136F787D33BA56B0495A40E86E671C940FD767EDD75EB 6001A49 S = 1071A56915DEE89E22E511975AA09D00CDC4AA7F5054CBE83F5977EE6F8E1CC3 1EC43FD:SHA-384、メッセージ= "サンプル" と

With SHA-512, message = "sample": k = 00F3B59FCB5C1A01A1A2A0019E98C244DFF61502D6E6B9C4E957EDDCEB258EF4 DBEF04A r = 1D0008CF4BA4A701BEF70771934C2A4A87386155A2354140E2ED52E18553C35B 47D9E50 s = 0D15F4FA1B7A4D41D9843578E22EF98773179103DC4FF0DD1F74A6B5642841B9 1056F78

SHA-512と、メッセージ= "サンプル":K = 00F3B59FCB5C1A01A1A2A0019E98C244DFF61502D6E6B9C4E957EDDCEB258EF4 DBEF04A R = 1D0008CF4BA4A701BEF70771934C2A4A87386155A2354140E2ED52E18553C35B 47D9E50 S = 0D15F4FA1B7A4D41D9843578E22EF98773179103DC4FF0DD1F74A6B5642841B9 1056F78

With SHA-1, message = "test": k = 168B5F8C0881D4026C08AC5894A2239D219FA9F4DA0600ADAA56D5A1781AF81F 08A726E r = 140932FA7307666A8CCB1E1A09656CC40F5932965841ABD5E8E43559D93CF231 1B02767 s = 16A2FD46DA497E5E739DED67F426308C45C2E16528BF2A17EB5D65964FD88B77 0FBB9C6

With SHA-1, message = "test": k = 168B5F8C0881D4026C08AC5894A2239D219FA9F4DA0600ADAA56D5A1781AF81F 08A726E r = 140932FA7307666A8CCB1E1A09656CC40F5932965841ABD5E8E43559D93CF231 1B02767 s = 16A2FD46DA497E5E739DED67F426308C45C2E16528BF2A17EB5D65964FD88B77 0FBB9C6

With SHA-224, message = "test": k = 045E13EA645CE01D9B25EA38C8A8A170E04C83BB7F231EE3152209FE10EC8B2E 565536C r = 0E72AF7E39CD72EF21E61964D87C838F977485FA6A7E999000AFA97A381B2445 FCEE541 s = 1644FF7D848DA1A040F77515082C27C763B1B4BF332BCF5D08251C6B57D80631 9778208

SHA-224を使用した場合、メッセージ= "test":k = 045E13EA645CE01D9B25EA38C8A8A170E04C83BB7F231EE3152209FE10EC8B2E 565536C r = 0E72AF7E39CD72EF21E61964D87C838F977485FA6ABFB761400B1104B1974B104B1176B104B1176BFFB761400B1104B1104B1540B1400B1400B1540B1400B1104B1540B1104B1540B1104B1540B1540B1540B1540B1540B1540B1540B1C98B1974B0154C1104B1C1C1C1C1C1C98C0F0f0c0c068bb68c68cbbc68bbc68なさいなさい

With SHA-256, message = "test": k = 0B585A7A68F51089691D6EDE2B43FC4451F66C10E65F134B963D4CBD4EB844B0 E1469A6 r = 158FAEB2470B306C57764AFC8528174589008449E11DB8B36994B607A65956A5 9715531 s = 0521BC667CA1CA42B5649E78A3D76823C678B7BB3CD58D2E93CD791D53043A6F 83F1FD1

SHA-256を使用した場合、メッセージ= "test":k = 0B585A7A68F51089691D6EDE2B43FC4451F66C10E65F134B963D4CBD4EB844B0 E1469A6 r = 158FAEB2470B306C57764AFC8528174589008449552B53A3DBE3DBE3DBE3DBEBDB3B3E9C3B3A3C3C3C3C3C3E3C0e0e0e0e0e0e0e0e0e0e0e0e8e8e8e8e5e8e3e00合成乗車

With SHA-384, message = "test": k = 1E88738E14482A09EE16A73D490A7FE8739DF500039538D5C4B6C8D6D7F208D6 CA56760 r = 1CC4DC5479E0F34C4339631A45AA690580060BF0EB518184C983E0E618C3B93A AB14BBE s = 0284D72FF8AFA83DE364502CBA0494BB06D40AE08F9D9746E747EA87240E589B A0683B7

With SHA-384, message = "test": k = 1E88738E14482A09EE16A73D490A7FE8739DF500039538D5C4B6C8D6D7F208D6 CA56760 r = 1CC4DC5479E0F34C4339631A45AA690580060BF0EB518184C983E0E618C3B93A AB14BBE s = 0284D72FF8AFA83DE364502CBA0494BB06D40AE08F9D9746E747EA87240E589B A0683B7

With SHA-512, message = "test": k = 00E5F24A223BD459653F682763C3BB322D4EE75DD89C63D4DC61518D543E7658 5076BBA r = 1E7912517C6899732E09756B1660F6B96635D638283DF9A8A11D30E008895D7F 5C9C7F3 s = 0887E75CBD0B7DD9DE30ED79BDB3D78E4F1121C5EAFF5946918F594F88D36364 4789DA7

SHA-512の場合、メッセージ= "test":k = 00E5F24A223BD459653F682763C3BB322D4EE75DD89C63D4DC61518D543E7658 5076BBA r = 1E7912517C6899732E09756B1660F6B96635D638283DF9F7F79D79F7D79F7D79F79D79F79D79F79D79F79F79C79D7FB3E79F7F7C75D79F7C8E7F75C3E7F75C3D7F8E7F75C3D7F8F7C75D7F75C7D75F7C75D7F75C7D75F8C7D75F7C7D88F7C7D7F8C7D7F8C7D8F6D0E0C7E7D8E7D8E7D8E0短0c

A.2.11. ECDSA, 409 Bits (Binary Field, Koblitz Curve)
A.2.11. ECDSA、409ビット(バイナリフィールド、コブリッツ曲線)

Key pair:


curve: NIST K-409

曲線:NIST K-409



private key:


   x = 29C16768F01D1B8A89FDA85E2EFD73A09558B92A178A2931F359E4D70AD853E5

public key: U = xG

公開鍵:U = xG

   Ux = 0CF923F523FE34A6E863D8BA45FB1FE6D784C8F219C414EEF4DB8362DBBD3CA7
   Uy = 13B1C374D5132978A1B1123EBBE9A5C54D1A9D56B09AFDB4ADE93CCD7C4D332E



   With SHA-1, message = "sample":
   k = 7866E5247F9A3556F983C86E81EDA696AC8489DB40A2862F278603982D304F08
   r = 7192EE99EC7AFE23E02CB1F9850D1ECE620475EDA6B65D04984029408EC1E5A6
   s = 1DE75DE97CBE740FC79A6B5B22BC2B7832C687E6960F0B8173D5D8BE2A75AC6C
   With SHA-224, message = "sample":
   k = 512340DB682C7B8EBE407BF1AA54194DFE85D49025FE0F632C9B8A06A996F2FC
   r = 41C8EDF39D5E4E76A04D24E6BFD4B2EC35F99CD2483478FD8B0A03E99379576E
   s = 659652EEAC9747BCAD58034B25362B6AA61836E1BA50E2F37630813050D43457
   With SHA-256, message = "sample":
   k = 782385F18BAF5A36A588637A76DFAB05739A14163BF723A4417B74BD1469D37A
   r = 49EC220D6D24980693E6D33B191532EAB4C5D924E97E305E2C1CCFE6F1EAEF96
   s = 1A4AB1DD9BAAA21F77C503E1B39E770FFD44718349D54BA4CF08F688CE89D7D7
   With SHA-384, message = "sample":
   k = 4DA637CB2E5C90E486744E45A73935DD698D4597E736DA332A06EDA8B26D5ABC
   r = 562BB99EE027644EC04E493C5E81B41F261F6BD18FB2FAE3AFEAD91FAB8DD44A
   s = 25BA5F28047DDDBDA7ED7E49DA31B62B20FD9C7E5B8988817BBF738B3F4DFDD2
   With SHA-512, message = "sample":
   k = 57055B293ECFDFE983CEF716166091E573275C53906A39EADC25C89C5EC8D7A7
   r = 16C7E7FB33B5577F7CF6F77762F0F2D531C6E7A3528BD2CF582498C1A48F2007
   s = 2729617EFBF80DA5D2F201AC7910D3404A992C39921C2F65F8CF4601392DFE93
   With SHA-1, message = "test":
   k = 545453D8DC05D220F9A12EF322D0B855E664C72835FABE8A41211453EB8A7CFF
   r = 565648A5BAD24E747A7D7531FA9DBDFCB184ECFEFDB00A319459242B68D0989E
   s = 7420BA6FF72ECC5C92B7CA0309258B5879F26393DB22753B9EC5DF905500A042
   With SHA-224, message = "test":
   k = 3C5352929D4EBE3CCE87A2DCE380F0D2B33C901E61ABC530DAF3506544AB0930
   r = 251DFE54EAEC8A781ADF8A623F7F36B4ABFC7EE0AE78C8406E93B5C3932A8120
   s = 77854C2E72EAA6924CC0B5F6751379D132569843B1C7885978DBBAA6678967F6
   With SHA-256, message = "test":
   k = 251E32DEE10ED5EA4AD7370DF3EFF091E467D5531CA59DE3AA791763715E1169
   r = 58075FF7E8D36844EED0FC3F78B7CFFDEEF6ADE5982D5636552A081923E24841
   s = 0A737469D013A31B91E781CE201100FDE1FA488ABF2252C025C678462D715AD3
   With SHA-384, message = "test":
   k = 11C540EA46C5038FE28BB66E2E9E9A04C9FE9567ADF33D56745953D44C1DC8B5
   r = 1C5C88642EA216682244E46E24B7CE9AAEF9B3F97E585577D158C3CBC3C59825
   s = 1D3FD721C35872C74514359F88AD983E170E5DE5B31AFC0BE12E9F4AB2B2538C
   With SHA-512, message = "test":
   k = 59527CE953BC09DF5E85155CAE7BB1D7F342265F41635545B06044F844ECB4FA
   r = 1A32CD7764149DF79349DBF79451F4585BB490BD63A200700D7111B45DDA4140
   s = 582AB1076CAFAE23A76244B82341AEFC4C6D8D8060A62A352C33187720C8A37F
A.2.12. ECDSA, 571 Bits (Binary Field, Koblitz Curve)
A.2.12. ECDSA、571ビット(バイナリフィールド、コブリッツ曲線)

Key pair:


curve: NIST K-571

curve: NIST K-571

q = 2000000000000000000000000000000000000000000000000000000000000000 0000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45 CFE778F637C1001 (qlen = 570 bits)

q = 2000000000000000000000000000000000000000000000000000000000000000 0000000131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45 CFE778F637C1001(qlen = 570ビット)

private key:


x = 0C16F58550D824ED7B95569D4445375D3A490BC7E0194C41A39DEB732C29396C DF1D66DE02DD1460A816606F3BEC0F32202C7BD18A32D87506466AA92032F131 4ED7B19762B0D22

x = 0C16F58550D824ED7B95569D4445375D3A490BC7E0194C41A39DEB732C29396C DF1D66DE02DD1460A816606F3BEC0F32202C7BD18A32D87506466AA92032F131 4ED7B19762B0D22

public key: U = xG

公開鍵:U = xG

Ux = 6CFB0DF7541CDD4C41EF319EA88E849EFC8605D97779148082EC991C463ED323 19596F9FDF4779C17CAF20EFD9BEB57E9F4ED55BFC52A2FA15CA23BC62B7BF01 9DB59793DD77318

Ux = 6CFB0DF7541CDD4C41EF319EA88E849EFC8605D97779148082EC991C463ED323 19596F9FDF4779C17CAF20EFD9BEB57E9F4ED55BFC52A2FA15CA23BC62B7BF01 9DB59793DD77318

Uy = 1CFC91102F7759A561BD8D5B51AAAEEC7F40E659D67870361990D6DE29F6B4F7 E18AE13BDE5EA5C1F77B23D676F44050C9DBFCCDD7B3756328DDA059779AAE84 46FC5158A75C227

Uy = 1CFC91102F7759A561BD8D5B51AAAEEC7F40E659D67870361990D6DE29F6B4F7 E18AE13BDE5EA5C1F77B23D676F44050C9DBFCCDD7B3756328DDA059779AAE84 46FC5158A75C227



With SHA-1, message = "sample": k = 17F7E360B21BEAE4A757A19ACA77FB404D273F05719A86EAD9D7B3F4D5ED7B46 30584BB153CF7DCD5A87CCA101BD7EA9ECA0CE5EE27CA985833560000BB52B6B BE068740A45B267 r = 0767913F96C82E38B7146A505938B79EC07E9AA3214377651BE968B52C039D3E 4837B4A2DE26C481C4E1DE96F4D9DE63845D9B32E26D0D332725678E3CE57F66 8A5E3108FB6CEA5 s = 109F89F55FA39FF465E40EBCF869A9B1DB425AEA53AB4ECBCE3C310572F79315 F5D4891461372A0C36E63871BEDDBB3BA2042C6410B67311F1A185589FF4C987 DBA02F9D992B9DF

With SHA-1, message = "sample": k = 17F7E360B21BEAE4A757A19ACA77FB404D273F05719A86EAD9D7B3F4D5ED7B46 30584BB153CF7DCD5A87CCA101BD7EA9ECA0CE5EE27CA985833560000BB52B6B BE068740A45B267 r = 0767913F96C82E38B7146A505938B79EC07E9AA3214377651BE968B52C039D3E 4837B4A2DE26C481C4E1DE96F4D9DE63845D9B32E26D0D332725678E3CE57F66 8A5E3108FB6CEA5 s = 109F89F55FA39FF465E40EBCF869A9B1DB425AEA53AB4ECBCE3C310572F79315 F5D4891461372A0C36E63871BEDDBB3BA2042C6410B67311F1A185589FF4C987 DBA02F9D992B9DF

With SHA-224, message = "sample": k = 0B599D068A1A00498EE0B9AD6F388521F594BD3F234E47F7A1DB6490D7B57D60 B0101B36F39CC22885F78641C69411279706F0989E6991E5D5B53619E43EFB39 7E25E0814EF02BC r = 010774B9F14DE6C9525131AD61531FA30987170D43782E9FB84FF0D70F093946 DF75ECB69D400FE39B12D58C67C19DCE96335CEC1D9AADE004FE5B498AB8A940 D46C8444348686A s = 06DFE9AA5FEA6CF2CEDC06EE1F9FD9853D411F0B958F1C9C519C90A85F6D24C1 C3435B3CDF4E207B4A67467C87B7543F6C0948DD382D24D1E48B3763EC27D4D3 2A0151C240CC5E0

SHA-224と、メッセージ= "サンプル":K = 0B599D068A1A00498EE0B9AD6F388521F594BD3F234E47F7A1DB6490D7B57D60 B0101B36F39CC22885F78641C69411279706F0989E6991E5D5B53619E43EFB39 7E25E0814EF02BC R = 010774B9F14DE6C9525131AD61531FA30987170D43782E9FB84FF0D70F093946 DF75ECB69D400FE39B12D58C67C19DCE96335CEC1D9AADE004FE5B498AB8A940 D46C8444348686A S = 06DFE9AA5FEA6CF2CEDC06EE1F9FD9853D411F0B958F1C9C519C90A85F6D24C1 C3435B3CDF4E207B4A67467C87B7543F6C0948DD382D24D1E48B3763EC27D4D3 2A0151C240CC5E0

With SHA-256, message = "sample": k = 0F79D53E63D89FB87F4D9E6DC5949F5D9388BCFE9EBCB4C2F7CE497814CF40E8 45705F8F18DBF0F860DE0B1CC4A433EF74A5741F3202E958C082E0B76E16ECD5 866AA0F5F3DF300 r = 1604BE98D1A27CEC2D3FA4BD07B42799E07743071E4905D7DCE7F6992B21A27F 14F55D0FE5A7810DF65CF07F2F2554658817E5A88D952282EA1B8310514C0B40 FFF46F159965168 s = 18249377C654B8588475510F7B797081F68C2F8CCCE49F730353B2DA3364B1CD 3E984813E11BB791824038EA367BA74583AB97A69AF2D77FA691AA694E348E15 DA76F5A44EC1F40

With SHA-256, message = "sample": k = 0F79D53E63D89FB87F4D9E6DC5949F5D9388BCFE9EBCB4C2F7CE497814CF40E8 45705F8F18DBF0F860DE0B1CC4A433EF74A5741F3202E958C082E0B76E16ECD5 866AA0F5F3DF300 r = 1604BE98D1A27CEC2D3FA4BD07B42799E07743071E4905D7DCE7F6992B21A27F 14F55D0FE5A7810DF65CF07F2F2554658817E5A88D952282EA1B8310514C0B40 FFF46F159965168 s = 18249377C654B8588475510F7B797081F68C2F8CCCE49F730353B2DA3364B1CD 3E984813E11BB791824038EA367BA74583AB97A69AF2D77FA691AA694E348E15 DA76F5A44EC1F40

With SHA-384, message = "sample": k = 0308253C022D25F8A9EBCD24459DD6596590BDEC7895618EEE8A2623A98D2A2B 2E7594EE6B7AD3A39D70D68CB4ED01CB28E2129F8E2CC0CC8DC7780657E28BCD 655F0BE9B7D35A2 r = 1E6D7FB237040EA1904CCBF0984B81B866DE10D8AA93B06364C4A46F6C9573FA 288C8BDDCC0C6B984E6AA75B42E7BF82FF34D51DFFBD7C87FDBFAD971656185B D12E4B8372F4BF1 s = 04F94550072ADA7E8C82B7E83577DD39959577799CDABCEA60E267F36F1BEB98 1ABF24E722A7F031582D2CC5D80DAA7C0DEEBBE1AC5E729A6DBB34A5D645B698 719FCA409FBA370

K = 0308253C022D25F8A9EBCD24459DD6596590BDEC7895618EEE8A2623A98D2A2B 2E7594EE6B7AD3A39D70D68CB4ED01CB28E2129F8E2CC0CC8DC7780657E28BCD 655F0BE9B7D35A2のR = 1E6D7FB237040EA1904CCBF0984B81B866DE10D8AA93B06364C4A46F6C9573FA 288C8BDDCC0C6B984E6AA75B42E7BF82FF34D51DFFBD7C87FDBFAD971656185B D12E4B8372F4BF1 S = 04F94550072ADA7E8C82B7E83577DD39959577799CDABCEA60E267F36F1BEB98 1ABF24E722A7F031582D2CC5D80DAA7C0DEEBBE1AC5E729A6DBB34A5D645B698 719FCA409FBA370:SHA-384、メッセージ= "サンプル" と

With SHA-512, message = "sample": k = 0C5EE7070AF55F84EBC43A0D481458CEDE1DCEBB57720A3C92F59B4941A044FE CFF4F703940F3121773595E880333772ACF822F2449E17C64DA286BCD65711DD 5DA44D7155BF004 r = 086C9E048EADD7D3D2908501086F3AF449A01AF6BEB2026DC381B39530BCDDBE 8E854251CBD5C31E6976553813C11213E4761CB8CA2E5352240AD9FB9C635D55 FAB13AE42E4EE4F s = 09FEE0A68F322B380217FCF6ABFF15D78C432BD8DD82E18B6BA877C01C860E24 410F5150A44F979920147826219766ECB4E2E11A151B6A15BB8E2E825AC95BCC A228D8A1C9D3568

With SHA-512, message = "sample": k = 0C5EE7070AF55F84EBC43A0D481458CEDE1DCEBB57720A3C92F59B4941A044FE CFF4F703940F3121773595E880333772ACF822F2449E17C64DA286BCD65711DD 5DA44D7155BF004 r = 086C9E048EADD7D3D2908501086F3AF449A01AF6BEB2026DC381B39530BCDDBE 8E854251CBD5C31E6976553813C11213E4761CB8CA2E5352240AD9FB9C635D55 FAB13AE42E4EE4F s = 09FEE0A68F322B380217FCF6ABFF15D78C432BD8DD82E18B6BA877C01C860E24 410F5150A44F979920147826219766ECB4E2E11A151B6A15BB8E2E825AC95BCC A228D8A1C9D3568

With SHA-1, message = "test": k = 1D056563469E933E4BE064585D84602D430983BFBFD6885A94BA484DF9A7AB03 1AD6AC090A433D8EEDC0A7643EA2A9BC3B6299E8ABA933B4C1F2652BB49DAEE8 33155C8F1319908 r = 1D055F499A3F7E3FC73D6E7D517B470879BDCB14ABC938369F23643C7B96D024 2C1FF326FDAF1CCC8593612ACE982209658E73C24C9EC493B785608669DA74A5 B7C9A1D8EA843BC s = 1621376C53CFE3390A0520D2C657B1FF0EBB10E4B9C2510EDC39D04FEBAF12B8 502B098A8B8F842EA6E8EB9D55CFEF94B7FF6D145AC3FFCE71BD978FEA3EF819 4D4AB5293A8F3EA

With SHA-1, message = "test": k = 1D056563469E933E4BE064585D84602D430983BFBFD6885A94BA484DF9A7AB03 1AD6AC090A433D8EEDC0A7643EA2A9BC3B6299E8ABA933B4C1F2652BB49DAEE8 33155C8F1319908 r = 1D055F499A3F7E3FC73D6E7D517B470879BDCB14ABC938369F23643C7B96D024 2C1FF326FDAF1CCC8593612ACE982209658E73C24C9EC493B785608669DA74A5 B7C9A1D8EA843BC s = 1621376C53CFE3390A0520D2C657B1FF0EBB10E4B9C2510EDC39D04FEBAF12B8 502B098A8B8F842EA6E8EB9D55CFEF94B7FF6D145AC3FFCE71BD978FEA3EF819 4D4AB5293A8F3EA

With SHA-224, message = "test": k = 1DA875065B9D94DBE75C61848D69578BCC267935792624F9887B53C9AF9E43CA BFC42E4C3F9A456BA89E717D24F1412F33CFD297A7A4D403B18B5438654C74D5 92D5022125E0C6B r = 18709BDE4E9B73D046CE0D48842C97063DA54DCCA28DCB087168FA37DA2BF5FD BE4720EE48D49EDE4DD5BD31AC0149DB8297BD410F9BC02A11EB79B60C8EE63A F51B65267D71881 s = 12D8B9E98FBF1D264D78669E236319D8FFD8426C56AFB10C76471EE88D7F0AB1 B158E685B6D93C850D47FB1D02E4B24527473DB60B8D1AEF26CEEBD3467B65A7 0FFDDC0DBB64D5F

SHA-224と、メッセージ= "テスト" K = 1DA875065B9D94DBE75C61848D69578BCC267935792624F9887B53C9AF9E43CA BFC42E4C3F9A456BA89E717D24F1412F33CFD297A7A4D403B18B5438654C74D5 92D5022125E0C6B R = 18709BDE4E9B73D046CE0D48842C97063DA54DCCA28DCB087168FA37DA2BF5FD BE4720EE48D49EDE4DD5BD31AC0149DB8297BD410F9BC02A11EB79B60C8EE63A F51B65267D71881 S = 12D8B9E98FBF1D264D78669E236319D8FFD8426C56AFB10C76471EE88D7F0AB1 B158E685B6D93C850D47FB1D02E4B24527473DB60B8D1AEF26CEEBD3467B65A7 0FFDDC0DBB64D5F

With SHA-256, message = "test": k = 04DDD0707E81BB56EA2D1D45D7FAFDBDD56912CAE224086802FEA1018DB306C4 FB8D93338DBF6841CE6C6AB1506E9A848D2C0463E0889268843DEE4ACB552CFF CB858784ED116B2 r = 1F5BF6B044048E0E310309FFDAC825290A69634A0D3592DBEE7BE71F69E45412 F766AC92E174CC99AABAA5C9C89FCB187DFDBCC7A26765DB6D9F1EEC8A6127BB DFA5801E44E3BEC s = 1B44CBFB233BFA2A98D5E8B2F0B2C27F9494BEAA77FEB59CDE3E7AE9CB2E385B E8DA7B80D7944AA71E0654E5067E9A70E88E68833054EED49F28283F02B22912 3995AF37A6089F0

K = 04DDD0707E81BB56EA2D1D45D7FAFDBDD56912CAE224086802FEA1018DB306C4 FB8D93338DBF6841CE6C6AB1506E9A848D2C0463E0889268843DEE4ACB552CFF CB858784ED116B2 R = 1F5BF6B044048E0E310309FFDAC825290A69634A0D3592DBEE7BE71F69E45412 F766AC92E174CC99AABAA5C9C89FCB187DFDBCC7A26765DB6D9F1EEC8A6127BB DFA5801E44E3BEC S = 1B44CBFB233BFA2A98D5E8B2F0B2C27F9494BEAA77FEB59CDE3E7AE9CB2E385B E8DA7B80D7944AA71E0654E5067E9A70E88E68833054EED49F28283F02B22912 3995AF37A6089F0:SHA-256、メッセージ= "テスト" と

With SHA-384, message = "test": k = 0141B53DC6E569D8C0C0718A58A5714204502FDA146E7E2133E56D19E905B794 13457437095DE13CF68B5CF5C54A1F2E198A55D974FC3E507AFC0ACF95ED391C 93CC79E3B3FE37C r = 11F61A6EFAB6D83053D9C52665B3542FF3F63BD5913E527BDBA07FBAF34BC766 C2EC83163C5273243AA834C75FDDD1BC8A2BEAD388CD06C4EBA1962D645EEB35 E92D44E8F2E081D s = 16BF6341876F051DF224770CC8BA0E4D48B3332568A2B014BC80827BAA89DE18 D1AEBC73E3BE8F85A8008C682AAC7D5F0E9FB5ECBEFBB637E30E4A0F226D2C2A A3E569BB54AB72B

K = 0141B53DC6E569D8C0C0718A58A5714204502FDA146E7E2133E56D19E905B794 13457437095DE13CF68B5CF5C54A1F2E198A55D974FC3E507AFC0ACF95ED391C 93CC79E3B3FE37C R = 11F61A6EFAB6D83053D9C52665B3542FF3F63BD5913E527BDBA07FBAF34BC766 C2EC83163C5273243AA834C75FDDD1BC8A2BEAD388CD06C4EBA1962D645EEB35 E92D44E8F2E081D S = 16BF6341876F051DF224770CC8BA0E4D48B3332568A2B014BC80827BAA89DE18 D1AEBC73E3BE8F85A8008C682AAC7D5F0E9FB5ECBEFBB637E30E4A0F226D2C2A A3E569BB54AB72B:SHA-384、メッセージ= "テスト" と

With SHA-512, message = "test": k = 14842F97F263587A164B215DD0F912C588A88DC4AB6AF4C530ADC1226F16E086 D62C14435E6BFAB56F019886C88922D2321914EE41A8F746AAA2B964822E4AC6 F40EE2492B66824 r = 0F1E50353A39EA64CDF23081D6BB4B2A91DD73E99D3DD5A1AA1C49B4F6E34A66 5EAD24FD530B9103D522609A395AF3EF174C85206F67EF84835ED1632E0F6BAB 718EA90DF9E2DA0 s = 0B385004D7596625028E3FDE72282DE4EDC5B4CE33C1127F21CC37527C90B730 7AE7D09281B840AEBCECAA711B00718103DDB32B3E9F6A9FBC6AF23E224A73B9 435F619D9C62527

K = 14842F97F263587A164B215DD0F912C588A88DC4AB6AF4C530ADC1226F16E086 D62C14435E6BFAB56F019886C88922D2321914EE41A8F746AAA2B964822E4AC6 F40EE2492B66824 R = 0F1E50353A39EA64CDF23081D6BB4B2A91DD73E99D3DD5A1AA1C49B4F6E34A66 5EAD24FD530B9103D522609A395AF3EF174C85206F67EF84835ED1632E0F6BAB 718EA90DF9E2DA0 S = 0B385004D7596625028E3FDE72282DE4EDC5B4CE33C1127F21CC37527C90B730 7AE7D09281B840AEBCECAA711B00718103DDB32B3E9F6A9FBC6AF23E224A73B9 435F619D9C62527:SHA-512、メッセージ= "テスト" と

A.2.13. ECDSA, 163 Bits (Binary Field, Pseudorandom Curve)
A.2.13. ECDSA, 163 Bits (Binary Field, Pseudorandom Curve)

Key pair:

Key pair:

curve: NIST B-163

曲線:NIST B-163

q = 40000000000000000000292FE77E70C12A4234C33 (qlen = 163 bits)

q = 40000000000000000000292FE77E70C12A4234C33(qlen = 163ビット)

private key:


   x = 35318FC447D48D7E6BC93B48617DDDEDF26AA658F

public key: U = xG

公開鍵:U = xG

   Ux = 126CF562D95A1D77D387BA75A3EA3A1407F23425A
   Uy = 7D7CB5273C94DA8CA93049AFDA18721C24672BD71



   With SHA-1, message = "sample":
   k = 0707A94C3D352E0A9FE49FB12F264992152A20004
   r = 153FEBD179A69B6122DEBF5BC61EB947B24C93526
   s = 37AC9C670F8CF18045049BAE7DD35553545C19E49
   With SHA-224, message = "sample":
   k = 3B24C5E2C2D935314EABF57A6484289B291ADFE3F
   r = 0A379E69C44F9C16EA3215EA39EB1A9B5D58CC955
   s = 04BAFF5308DA2A7FE2C1742769265AD3ED1D24E74
   With SHA-256, message = "sample":
   k = 3D7086A59E6981064A9CDB684653F3A81B6EC0F0B
   r = 134E00F78FC1CB9501675D91C401DE20DDF228CDC
   s = 373273AEC6C36CB7BAFBB1903A5F5EA6A1D50B624
   With SHA-384, message = "sample":
   k = 3B1E4443443486C7251A68EF184A936F05F8B17C7
   r = 29430B935AF8E77519B0CA4F6903B0B82E6A21A66
   s = 1EA1415306E9353FA5AA54BC7C2581DFBB888440D
   With SHA-512, message = "sample":
   k = 2EDF5CFCAC7553C17421FDF54AD1D2EF928A879D2
   r = 0B2F177A99F9DF2D51CCAF55F015F326E4B65E7A0
   s = 0DF1FB4487E9B120C5E970EFE48F55E406306C3A1
   With SHA-1, message = "test":
   k = 10024F5B324CBC8954BA6ADB320CD3AB9296983B4
   r = 256D4079C6C7169B8BC92529D701776A269D56308
   s = 341D3FFEC9F1EB6A6ACBE88E3C86A1C8FDEB8B8E1
   With SHA-224, message = "test":
   k = 34F46DE59606D56C75406BFB459537A7CC280AA62
   r = 28ECC6F1272CE80EA59DCF32F7AC2D861BA803393
   s = 0AD4AE2C06E60183C1567D2B82F19421FE3053CE2
   With SHA-256, message = "test":
   k = 38145E3FFCA94E4DDACC20AD6E0997BD0E3B669D2
   r = 227DF377B3FA50F90C1CB3CDCBBDBA552C1D35104
   s = 1F7BEAD92583FE920D353F368C1960D0E88B46A56
   With SHA-384, message = "test":
   k = 375813210ECE9C4D7AB42DDC3C55F89189CF6DFFD
   r = 11811DAFEEA441845B6118A0DFEE8A0061231337D
   s = 36258301865EE48C5C6F91D63F62695002AB55B57
   With SHA-512, message = "test":
   k = 25AD8B393BC1E9363600FDA1A2AB6DF40079179A3
   r = 3B6BB95CA823BE2ED8E3972FF516EB8972D765571
   s = 13DC6F420628969DF900C3FCC48220B38BE24A541
A.2.14. ECDSA, 233 Bits (Binary Field, Pseudorandom Curve)
A.2.14. ECDSA, 233 Bits (Binary Field, Pseudorandom Curve)

Key pair:


curve: NIST B-233

曲線:NIST B-233

q = 1000000000000000000000000000013E974E72F8A6922031D2603CFE0D7 (qlen = 233 bits)

q = 1000000000000000000000000000013E974E72F8A6922031D2603CFE0D7(qlen = 233ビット)

private key:


   x = 07ADC13DD5BF34D1DDEEB50B2CE23B5F5E6D18067306D60C5F6FF11E5D3

public key: U = xG

公開鍵:U = xG

   Ux = 0FB348B3246B473AA7FBB2A01B78D61B62C4221D0F9AB55FC72DB3DF478
   Uy = 1162FA1F6C6ACF7FD8D19FC7D74BDD9104076E833898BC4C042A6E6BEBF



   With SHA-1, message = "sample":
   k = 0A4E0B67A3A081C1B35D7BECEB5FE72A918B422B907145DB5416ED751CE
   r = 015CC6FD78BB06E0878E71465515EA5A21A2C18E6FC77B4B158DBEB3944
   s = 0822A4A6C2EB2DF213A5E90BF40377956365EE8C4B4A5A4E2EB9270CB6A
   With SHA-224, message = "sample":
   k = 0F2B1C1E80BEB58283AAA79857F7B83BDF724120D0913606FD07F7FFB2C
   r = 05D9920B53471148E10502AB49AB7A3F11084820A074FD89883CF51BC1A
   s = 04D3938900C0A9AAA7080D1DFEB56CFB0FADABE4214536C7ED5117ED13A
   With SHA-256, message = "sample":
   k = 034A53897B0BBDB484302E19BF3F9B34A2ABFED639D109A388DC52006B5
   r = 0A797F3B8AEFCE7456202DF1E46CCC291EA5A49DA3D4BDDA9A4B62D5E0D
   s = 01F6F81DA55C22DA4152134C661588F4BD6F82FDBAF0C5877096B070DC2
   With SHA-384, message = "sample":
   k = 04D4670B28990BC92EEB49840B482A1FA03FE028D09F3D21F89C67ECA85
   r = 015E85A8D46225DD7E314A1C4289731FC14DECE949349FE535D11043B85
   s = 03F189D37F50493EFD5111A129443A662AB3C6B289129AD8C0CAC85119C
   With SHA-512, message = "sample":
   k = 0DE108AAADA760A14F42C057EF81C0A31AF6B82E8FBCA8DC86E443AB549
   r = 03B62A4BF783919098B1E42F496E65F7621F01D1D466C46940F0F132A95
   s = 0F4BE031C6E5239E7DAA014CBBF1ED19425E49DAEB426EC9DF4C28A2E30
   With SHA-1, message = "test":
   k = 0250C5C90A4E2A3F8849FEBA87F0D0AE630AB18CBABB84F4FFFB36CEAC0
   r = 02F1FEDC57BE203E4C8C6B8C1CEB35E13C1FCD956AB41E3BD4C8A6EFB1F
   s = 05738EC8A8EDEA8E435EE7266AD3EDE1EEFC2CEBE2BE1D614008D5D2951
   With SHA-224, message = "test":
   k = 07BDB6A7FD080D9EC2FC84BFF9E3E15750789DC04290C84FED00E109BBD
   r = 0CCE175124D3586BA7486F7146894C65C2A4A5A1904658E5C7F9DF5FA5D
   s = 08804B456D847ACE5CA86D97BF79FD6335E5B17F6C0D964B5D0036C867E
   With SHA-256, message = "test":
   k = 00376886E89013F7FF4B5214D56A30D49C99F53F211A3AFE01AA2BDE12D
   r = 035C3D6DFEEA1CFB29B93BE3FDB91A7B130951770C2690C16833A159677
   s = 0600F7301D12AB376B56D4459774159ADB51F97E282FF384406AFD53A02
   With SHA-384, message = "test":
   k = 03726870DE75613C5E529E453F4D92631C03D08A7F63813E497D4CB3877
   r = 061602FC8068BFD5FB86027B97455D200EC603057446CCE4D76DB8EF42C
   s = 03396DD0D59C067BB999B422D9883736CF9311DFD6951F91033BD03CA8D
   With SHA-512, message = "test":
   k = 09CE5810F1AC68810B0DFFBB6BEEF2E0053BB937969AE7886F9D064A8C4
   r = 07E12CB60FDD614958E8E34B3C12DDFF35D85A9C5800E31EA2CC2EF63B1
   s = 0E8970FD99D836F3CC1C807A2C58760DE6EDAA23705A82B9CB1CE93FECC
A.2.15. ECDSA, 283 Bits (Binary Field, Pseudorandom Curve)
A.2.15. ECDSA、283ビット(バイナリフィールド、疑似ランダム曲線)

Key pair:


curve: NIST B-283

curve: NIST B-283

q = 3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CE FADB307 (qlen = 282 bits)


private key:


x = 14510D4BC44F2D26F4553942C98073C1BD35545CEABB5CC138853C5158D2729E A408836

x = 14510D4BC44F2D26F4553942C98073C1BD35545CEABB5CC138853C5158D2729E A408836

public key: U = xG

公開鍵:U = xG

Ux = 17E3409A13C399F0CA8A192F028D46E3446BCFFCDF51FF8A905ED2DED786E74F 9C3E8A9

Ux = 17E3409A13C399F0CA8A192F028D46E3446BCFFCDF51FF8A905ED2DED786E74F 9C3E8A9

Uy = 47EFCBCC31C01D86D1992F7BFAC0277DBD02A6D289274099A2C0F039C8F59F31 8371B0E

Uy = 47EFCBCC31C01D86D1992F7BFAC0277DBD02A6D289274099A2C0F039C8F59F31 8371B0E



With SHA-1, message = "sample": k = 277F389559667E8AE4B65DC056F8CE2872E1917E7CC59D17D485B0B98343206F BCCD441 r = 201E18D48C6DB3D5D097C4DCE1E25587E1501FC3CF47BDB5B4289D79E273D6A9 ACB8285 s = 151AE05712B024CE617358260774C8CA8B0E7A7E72EF8229BF2ACE7609560CB3 0322C4F

With SHA-1, message = "sample": k = 277F389559667E8AE4B65DC056F8CE2872E1917E7CC59D17D485B0B98343206F BCCD441 r = 201E18D48C6DB3D5D097C4DCE1E25587E1501FC3CF47BDB5B4289D79E273D6A9 ACB8285 s = 151AE05712B024CE617358260774C8CA8B0E7A7E72EF8229BF2ACE7609560CB3 0322C4F

With SHA-224, message = "sample": k = 14CC8FCFEECD6B999B4DC6084EBB06FDED0B44D5C507802CC7A5E9ECF36E69DA 6AE23C6 r = 143E878DDFD4DF40D97B8CD638B3C4706501C2201CF7108F2FB91478C11D6947 3246925 s = 0CBF1B9717FEEA3AABB09D9654110144267098E0E1E8D0289A6211BE0EEDFDD8 6A3DB79

SHA-224を使用した場合、メッセージ= "sample":k = 14CC8FCFEECD6B999B4DC6084EBB06FDED0B44D5C507802CC7A5E9ECF36E69DA 6AE23C6 r = 143E878DDFD4DF40D97B8CD638B3C4706501289220CF14108A1104EA49E010432BEABE1974C1974EA09E0A0104A0104A049E0E0E0

With SHA-256, message = "sample": k = 38C9D662188982943E080B794A4CFB0732DBA37C6F40D5B8CFADED6FF31C5452 BA3F877 r = 29FD82497FB3E5CEF65579272138DE59E2B666B8689466572B3B69A172CEE83B E145659 s = 05A89D9166B40795AF0FE5958201B9C0523E500013CA12B4840EA2BC53F25F9B 3CE87C0

With SHA-256, message = "sample": k = 38C9D662188982943E080B794A4CFB0732DBA37C6F40D5B8CFADED6FF31C5452 BA3F877 r = 29FD82497FB3E5CEF65579272138DE59E2B666B8689466572B3B69A172CEE83B E145659 s = 05A89D9166B40795AF0FE5958201B9C0523E500013CA12B4840EA2BC53F25F9B 3CE87C0

With SHA-384, message = "sample": k = 21B7265DEBF90E6F988CFFDB62B121A02105226C652807CC324ED6FB119A287A 72680AB r = 2F00689C1BFCD2A8C7A41E0DE55AE182E6463A152828EF89FE3525139B660329 4E69353 s = 1744514FE0A37447250C8A329EAAADA81572226CABA16F39270EE5DD03F27B1F 665EB5D

SHA-384の場合、メッセージ= "sample":k = 21B7265DEBF90E6F988CFFDB62B121A02105226C652807CC324ED6FB119A287A 72680AB r = 2F00689C1BFCD2A8C7A41E0DE55AE182E6463A152828EF89FE3525139B660329 4E69353AABEAA250ACAAAA270AA12A120AAFA270A03A14A14AA540AAA120AA120A3A540A3A9A540A3A9A120AA3A9A120A3A9AA540A3C9C9A9A9A9A0C0C0A0

With SHA-512, message = "sample": k = 20583259DC179D9DA8E5387E89BFF2A3090788CF1496BCABFE7D45BB120B0C81 1EB8980 r = 0DA43A9ADFAA6AD767998A054C6A8F1CF77A562924628D73C62761847AD8286E 0D91B47 s = 1D118733AE2C88357827CAFC6F68ABC25C80C640532925E95CFE66D40F8792F3 AC44C42

SHA-512と、メッセージ= "サンプル":K = 20583259DC179D9DA8E5387E89BFF2A3090788CF1496BCABFE7D45BB120B0C81 1EB8980 R = 0DA43A9ADFAA6AD767998A054C6A8F1CF77A562924628D73C62761847AD8286E 0D91B47 S = 1D118733AE2C88357827CAFC6F68ABC25C80C640532925E95CFE66D40F8792F3 AC44C42

With SHA-1, message = "test": k = 0185C57A743D5BA06193CE2AA47B07EF3D6067E5AE1A6469BCD3FC510128BA56 4409D82 r = 05A408133919F2CDCDBE5E4C14FBC706C1F71BADAFEF41F5DE4EC27272FC1CA9 366FBB2 s = 012966272872C097FEA7BCE64FAB1A81982A773E26F6E4EF7C99969846E67CA9 CBE1692

SHA-1を使用した場合、メッセージ= "test":k = 0185C57A743D5BA06193CE2AA47B07EF3D6067E5AE1A6469BCD3FC510128BA56 4409D82 r = 05A408133919F2CDCDBE5E4C14FBC706C1F71BADAFEF41F5DE4EC27272A2C9A6A6A6A9C926F6DE4EC27272A2C9A6A6A9B9C9AFAB9C9A6A9AB9C9A6B9C9A6B9C9A6A9C96A6B9C9A6B9C9A9C096A6E9A9C096B0A9C0A9F0E6E0E0E0E

With SHA-224, message = "test": k = 2E5C1F00677A0E015EC3F799FA9E9A004309DBD784640EAAF5E1CE64D3045B9F E9C1FA1 r = 08F3824E40C16FF1DDA8DC992776D26F4A5981AB5092956C4FDBB4F1AE0A711E EAA10E5 s = 0A64B91EFADB213E11483FB61C73E3EF63D3B44EEFC56EA401B99DCC60CC28E9 9F0F1FA

K = 2E5C1F00677A0E015EC3F799FA9E9A004309DBD784640EAAF5E1CE64D3045B9F E9C1FA1 R = 08F3824E40C16FF1DDA8DC992776D26F4A5981AB5092956C4FDBB4F1AE0A711E EAA10E5 S = 0A64B91EFADB213E11483FB61C73E3EF63D3B44EEFC56EA401B99DCC60CC28E9 9F0F1FA:SHA-224、メッセージ= "テスト" と

With SHA-256, message = "test": k = 018A7D44F2B4341FEFE68F6BD8894960F97E08124AAB92C1FFBBE90450FCC935 6C9AAA5 r = 3597B406F5329D11A79E887847E5EC60861CCBB19EC61F252DB7BD549C699951 C182796 s = 0A6A100B997BC622D91701D9F5C6F6D3815517E577622DA69D3A0E8917C1CBE6 3ACD345

SHA-256を使用した場合、メッセージ= "test":k = 018A7D44F2B4341FEFE68F6BD8894960F97E08124AAB92C1FFBBE90450FCC935 6C9AAA5 r = 3597B406F5329D11A79E887847E5EC60861CC6D17AB700A6700A175A6A175A6700A756A17A756A005D175A6A175A6974C6956A6974A6974A6974A6974C1956A6974A6974A6974A6176A6974A6974C1956A622D1

With SHA-384, message = "test": k = 3C75397BA4CF1B931877076AF29F2E2F4231B117AB4B8E039F7F9704DE1BD352 2F150B6 r = 1BB490926E5A1FDC7C5AA86D0835F9B994EDA315CA408002AF54A298728D422E BF59E4C s = 36C682CFC9E2C89A782BFD3A191609D1F0C1910D5FD6981442070393159D65FB CC0A8BA

SHA-384、メッセージを= "テスト":K = 3C75397BA4CF1B931877076AF29F2E2F4231B117AB4B8E039F7F9704DE1BD352 2F150B6 R = 1BB490926E5A1FDC7C5AA86D0835F9B994EDA315CA408002AF54A298728D422E BF59E4C S = 36C682CFC9E2C89A782BFD3A191609D1F0C1910D5FD6981442070393159D65FB CC0A8BA

With SHA-512, message = "test": k = 14E66B18441FA54C21E3492D0611D2B48E19DE3108D915FD5CA08E786327A267 5F11074 r = 19944AA68F9778C2E3D6E240947613E6DA60EFCE9B9B2C063FF5466D72745B5A 0B25BA2 s = 03F1567B3C5B02DF15C874F0EE22850824693D5ADC4663BAA19E384E550B1DD4 1F31EE6

SHA-512を使用した場合、メッセージ= "test":k = 14E66B18441FA54C21E3492D0611D2B48E19DE3108D915FD5CA08E786327A267 5F11074 r = 19944AA68F9778C2E3D6E240947613E6DA60EFCE9B5B5B5B5ABF3BF5BBF540B03A5B5A5B540C0154A5B3B3C540C0540C0540

A.2.16. ECDSA, 409 Bits (Binary Field, Pseudorandom Curve)
A.2.16. ECDSA、409ビット(バイナリフィールド、疑似ランダム曲線)

Key pair:


curve: NIST B-409

曲線:NIST B-409

q = 10000000000000000000000000000000000000000000000000001E2AAD6A612F 33307BE5FA47C3C9E052F838164CD37D9A21173 (qlen = 409 bits)

q = 10000000000000000000000000000000000000000000000000001E2AAD6A612F 33307BE5FA47C3C9E052F838164CD37D9A21173 (qlen = 409 bits)

private key:


   x = 0494994CC325B08E7B4CE038BD9436F90B5E59A2C13C3140CD3AE07C04A01FC4

public key: U = xG

public key: U = xG

   Ux = 1A7055961CF1DA4B9A015B18B1524EF01FDD9B93FAEFC26FB1F2F828A7227B70
   Uy = 18105C042F290736088F30AEC7AE7732A45DE47BCE0940113AB8132516D1E059



   With SHA-1, message = "sample":
   k = 042D8A2B34402757EB2CCFDDC3E6E96A7ADD3FDA547FC10A0CB77CFC720B4F9E
   r = 0D8783188E1A540E2022D389E1D35B32F56F8C2BB5636B8ABF7718806B27A713
   s = 03A6B4A80E204DB0DE12E7415C13C9EC091C52935658316B4A0C591216A38791
   With SHA-224, message = "sample":
   k = 0C933F1DC4C70838C2AD16564715ACAF545BCDD8DC203D25AF3EC63949C65CB2
   r = 0EE4F39ACC2E03CE96C3D9FCBAFA5C22C89053662F8D4117752A9B10F09ADFDA
   s = 00A2B83265B456A430A8BF27DCC8A9488B3F126C10F0D6D64BF7B8A218FAAF20
   With SHA-256, message = "sample":
   k = 08EC42D13A3909A20C41BEBD2DFED8CACCE56C7A7D1251DF43F3E9E289DAE00E
   r = 02D8B1B31E33E74D7EB46C30FDE5AD2CA04EC8FE08FBA0E73BA5E568953AC5EA
   s = 079F7D471E6CB73234AF7F7C381D2CE15DE35BAF8BB68393B73235B3A26EC2DF
   With SHA-384, message = "sample":
   k = 0DA881BCE3BA851485879EF8AC585A63F1540B9198ECB8A1096D70CB25A104E2
   r = 07BC638B7E7CE6FEE5E9C64A0F966D722D01BB4BC3F3A35F30D4CDDA92DFC5F7
   s = 06D904429850521B28A32CBF55C7C0FDF35DC4E0BDA2552C7BF68A171E970E67
   With SHA-512, message = "sample":
   k = 0750926FFAD7FF5DE85DF7960B3A4F9E3D38CF5A049BFC89739C48D42B34FBEE
   r = 05D178DECAFD2D02A3DA0D8BA1C4C1D95EE083C760DF782193A9F7B4A8BE6FC5
   s = 013B7581E98F6A63FBBCB3E49BCDA60F816DB230B888506D105DC229600497C3
   With SHA-1, message = "test":
   k = 017E167EAB1850A3B38EE66BFE2270F2F6BFDAC5E2D227D47B20E75F0719161E
   r = 049F54E7C10D2732B4638473053782C6919218BBEFCEC8B51640FC193E832291
   s = 0499E267DEC84E02F6F108B10E82172C414F15B1B7364BE8BFD66ADC0C5DE23F
   With SHA-224, message = "test":
   k = 01ADEB94C19951B460A146B8275D81638C07735B38A525D76023AAF26AA8A058
   r = 0B1527FFAA7DD7C7E46B628587A5BEC0539A2D04D3CF27C54841C2544E1BBDB4
   s = 0442C68C044868DF4832C807F1EDDEBF7F5052A64B826FD03451440794063F52
   With SHA-256, message = "test":
   k = 06EBA3D58D0E0DFC406D67FC72EF0C943624CF40019D1E48C3B54CCAB0594AFD
   r = 0BB27755B991D6D31757BCBF68CB01225A38E1CFA20F775E861055DD108ED7EA
   s = 0C5BE90980E7F444B5F7A12C9E9AC7A04CA81412822DD5AD1BE7C45D5032555E
   With SHA-384, message = "test":
   k = 0A45B787DB44C06DEAB846511EEDBF7BFCFD3BD2C11D965C92FC195F67328F36
   r = 04EFEB7098772187907C87B33E0FBBA4584226C50C11E98CA7AAC6986F8D3BE0
   s = 09574102FEB3EF87E6D66B94119F5A6062950FF4F902EA1E6BD9E2037F33FF99
   With SHA-512, message = "test":
   k = 0B90F8A0E757E81D4EA6891766729C96A6D01F9AEDC0D334932D1F81CC4E1973
   r = 07E0249C68536AE2AEC2EC30090340DA49E6DC9E9EEC8F85E5AABFB234B6DA7D
   s = 08125B5A03FB44AE81EA46D446130C2A415ECCA265910CA69D55F2453E16CD7B
A.2.17. ECDSA, 571 Bits (Binary Field, Pseudorandom Curve)
A.2.17. ECDSA、571ビット(バイナリフィールド、疑似ランダム曲線)

Key pair:


curve: NIST B-571

curve: NIST B-571



private key:

private key:

x = 028A04857F24C1C082DF0D909C0E72F453F2E2340CCB071F0E389BCA2575DA19 124198C57174929AD26E348CF63F78D28021EF5A9BF2D5CBEAF6B7CCB6C4DA82 4DD5C82CFB24E11

x = 028A04857F24C1C082DF0D909C0E72F453F2E2340CCB071F0E389BCA2575DA19 124198C57174929AD26E348CF63F78D28021EF5A9BF2D5CBEAF6B7CCB6C4DA82 4DD5C82CFB24E11

public key: U = xG

公開鍵:U = xG

Ux = 4B4B3CE9377550140B62C1061763AA524814DDCEF37B00CD5CDE94F7792BB0E9 6758E55DA2E9FEA8FF2A8B6830AE1D57A9CA7A77FCB0836BF43EA5454CDD9FEA D5CCFE7375C6A83

Ux = 4B4B3CE9377550140B62C1061763AA524814DDCEF37B00CD5CDE94F7792BB0E9 6758E55DA2E9FEA8FF2A8B6830AE1D57A9CA7A77FCB0836BF43EA5454CDD9FEA D5CCFE7375C6A83

Uy = 4453B18F261E7A0E7570CD72F235EA750438E43946FBEBD2518B696954767AA7 849C1719E18E1C51652C28CA853426F15C09AA4B579487338ABC7F33768FADD6 1B5A3A6443A8189

Uy = 4453B18F261E7A0E7570CD72F235EA750438E43946FBEBD2518B696954767AA7 849C1719E18E1C51652C28CA853426F15C09AA4B579487338ABC7F33768FADD6 1B5A3A6443A8189



With SHA-1, message = "sample": k = 2669FAFEF848AF67D437D4A151C3C5D3F9AA8BB66EDC35F090C9118F95BA0041 B0993BE2EF55DAAF36B5B3A737C40DB1F6E3D93D97B8419AD6E1BB8A5D4A0E9B 2E76832D4E7B862 r = 147D3EB0EDA9F2152DFD014363D6A9CE816D7A1467D326A625FC4AB0C786E1B7 4DDF7CD4D0E99541391B266C704BB6B6E8DCCD27B460802E0867143727AA4155 55454321EFE5CB6 s = 17319571CAF533D90D2E78A64060B9C53169AB7FC908947B3EDADC54C79CCF0A 7920B4C64A4EAB6282AFE9A459677CDA37FD6DD50BEF18709590FE18B923BDF7 4A66B189A850819

With SHA-1, message = "sample": k = 2669FAFEF848AF67D437D4A151C3C5D3F9AA8BB66EDC35F090C9118F95BA0041 B0993BE2EF55DAAF36B5B3A737C40DB1F6E3D93D97B8419AD6E1BB8A5D4A0E9B 2E76832D4E7B862 r = 147D3EB0EDA9F2152DFD014363D6A9CE816D7A1467D326A625FC4AB0C786E1B7 4DDF7CD4D0E99541391B266C704BB6B6E8DCCD27B460802E0867143727AA4155 55454321EFE5CB6 s = 17319571CAF533D90D2E78A64060B9C53169AB7FC908947B3EDADC54C79CCF0A 7920B4C64A4EAB6282AFE9A459677CDA37FD6DD50BEF18709590FE18B923BDF7 4A66B189A850819

With SHA-224, message = "sample": k = 2EAFAD4AC8644DEB29095BBAA88D19F31316434F1766AD4423E0B54DD2FE0C05 E307758581B0DAED2902683BBC7C47B00E63E3E429BA54EA6BA3AEC33A94C9A2 4A6EF8E27B7677A r = 10F4B63E79B2E54E4F4F6A2DBC786D8F4A143ECA7B2AD97810F6472AC6AE2085 3222854553BE1D44A7974599DB7061AE8560DF57F2675BE5F9DD94ABAF3D47F1 582B318E459748B s = 3BBEA07C6B269C2B7FE9AE4DDB118338D0C2F0022920A7F9DCFCB7489594C03B 536A9900C4EA6A10410007222D3DAE1A96F291C4C9275D75D98EB290DC0EEF17 6037B2C7A7A39A3

With SHA-224, message = "sample": k = 2EAFAD4AC8644DEB29095BBAA88D19F31316434F1766AD4423E0B54DD2FE0C05 E307758581B0DAED2902683BBC7C47B00E63E3E429BA54EA6BA3AEC33A94C9A2 4A6EF8E27B7677A r = 10F4B63E79B2E54E4F4F6A2DBC786D8F4A143ECA7B2AD97810F6472AC6AE2085 3222854553BE1D44A7974599DB7061AE8560DF57F2675BE5F9DD94ABAF3D47F1 582B318E459748B s = 3BBEA07C6B269C2B7FE9AE4DDB118338D0C2F0022920A7F9DCFCB7489594C03B 536A9900C4EA6A10410007222D3DAE1A96F291C4C9275D75D98EB290DC0EEF17 6037B2C7A7A39A3

With SHA-256, message = "sample": k = 15C2C6B7D1A070274484774E558B69FDFA193BDB7A23F27C2CD24298CE1B22A6 CC9B7FB8CABFD6CF7C6B1CF3251E5A1CDDD16FBFED28DE79935BB2C631B8B8EA 9CC4BCC937E669E r = 213EF9F3B0CFC4BF996B8AF3A7E1F6CACD2B87C8C63820000800AC787F17EC99 C04BCEDF29A8413CFF83142BB88A50EF8D9A086AF4EB03E97C567500C21D8657 14D832E03C6D054 s = 3D32322559B094E20D8935E250B6EC139AC4AAB77920812C119AF419FB62B332 C8D226C6C9362AE3C1E4AABE19359B8428EA74EC8FBE83C8618C2BCCB6B43FBA A0F2CCB7D303945

SHA-256、メッセージ= "サンプル":K = 15C2C6B7D1A070274484774E558B69FDFA193BDB7A23F27C2CD24298CE1B22A6 CC9B7FB8CABFD6CF7C6B1CF3251E5A1CDDD16FBFED28DE79935BB2C631B8B8EA 9CC4BCC937E669E R = 213EF9F3B0CFC4BF996B8AF3A7E1F6CACD2B87C8C63820000800AC787F17EC99 C04BCEDF29A8413CFF83142BB88A50EF8D9A086AF4EB03E97C567500C21D8657 14D832E03C6D054 S = 3D32322559B094E20D8935E250B6EC139AC4AAB77920812C119AF419FB62B332 C8D226C6C9362AE3C1E4AABE19359B8428EA74EC8FBE83C8618C2BCCB6B43FBA A0F2CCB7D303945

With SHA-384, message = "sample": k = 0FEF0B68CB49453A4C6ECBF1708DBEEFC885C57FDAFB88417AAEFA5B1C35017B 4B498507937ADCE2F1D9EFFA5FE8F5AEB116B804FD182A6CF1518FDB62D53F60 A0FF6EB707D856B r = 375D8F49C656A0BBD21D3F54CDA287D853C4BB1849983CD891EF6CD6BB56A62B 687807C16685C2C9BCA2663C33696ACCE344C45F3910B1DF806204FF731ECB28 9C100EF4D1805EC s = 1CDEC6F46DFEEE44BCE71D41C60550DC67CF98D6C91363625AC2553E4368D2DF B734A8E8C72E118A76ACDB0E58697940A0F3DF49E72894BD799450FC9E550CC0 4B9FF9B0380021C

SHA-384と、メッセージ= "サンプル":K = 0FEF0B68CB49453A4C6ECBF1708DBEEFC885C57FDAFB88417AAEFA5B1C35017B 4B498507937ADCE2F1D9EFFA5FE8F5AEB116B804FD182A6CF1518FDB62D53F60 A0FF6EB707D856B R = 375D8F49C656A0BBD21D3F54CDA287D853C4BB1849983CD891EF6CD6BB56A62B 687807C16685C2C9BCA2663C33696ACCE344C45F3910B1DF806204FF731ECB28 9C100EF4D1805EC S = 1CDEC6F46DFEEE44BCE71D41C60550DC67CF98D6C91363625AC2553E4368D2DF B734A8E8C72E118A76ACDB0E58697940A0F3DF49E72894BD799450FC9E550CC0 4B9FF9B0380021C

With SHA-512, message = "sample": k = 3FF373833A06C791D7AD586AFA3990F6EF76999C35246C4AD0D519BFF180CA18 80E11F2FB38B764854A0AE3BECDDB50F05AC4FCEE542F207C0A6229E2E19652F 0E647B9C4882193 r = 1C26F40D940A7EAA0EB1E62991028057D91FEDA0366B606F6C434C361F04E545 A6A51A435E26416F6838FFA260C617E798E946B57215284182BE55F29A355E60 24FE32A47289CF0 s = 3691DE4369D921FE94EDDA67CB71FBBEC9A436787478063EB1CC778B3DCDC1C4 162662752D28DEEDF6F32A269C82D1DB80C87CE4D3B662E03AC347806E3F19D1 8D6D4DE7358DF7E

SHA-512と、メッセージ= "サンプル":K = 3FF373833A06C791D7AD586AFA3990F6EF76999C35246C4AD0D519BFF180CA18 80E11F2FB38B764854A0AE3BECDDB50F05AC4FCEE542F207C0A6229E2E19652F 0E647B9C4882193 R = 1C26F40D940A7EAA0EB1E62991028057D91FEDA0366B606F6C434C361F04E545 A6A51A435E26416F6838FFA260C617E798E946B57215284182BE55F29A355E60 24FE32A47289CF0 S = 3691DE4369D921FE94EDDA67CB71FBBEC9A436787478063EB1CC778B3DCDC1C4 162662752D28DEEDF6F32A269C82D1DB80C87CE4D3B662E03AC347806E3F19D1 8D6D4DE7358DF7E

With SHA-1, message = "test": k = 019B506FD472675A7140E429AA5510DCDDC21004206EEC1B39B28A688A8FD324 138F12503A4EFB64F934840DFBA2B4797CFC18B8BD0B31BBFF3CA66A4339E4EF 9D771B15279D1DC r = 133F5414F2A9BC41466D339B79376038A64D045E5B0F792A98E5A7AA87E0AD01 6419E5F8D176007D5C9C10B5FD9E2E0AB8331B195797C0358BA05ECBF24ACE59 C5F368A6C0997CC s = 3D16743AE9F00F0B1A500F738719C5582550FEB64689DA241665C4CE4F328BA0 E34A7EF527ED13BFA5889FD2D1D214C11EB17D6BC338E05A56F41CAFF1AF7B8D 574DB62EF0D0F21

With SHA-1, message = "test": k = 019B506FD472675A7140E429AA5510DCDDC21004206EEC1B39B28A688A8FD324 138F12503A4EFB64F934840DFBA2B4797CFC18B8BD0B31BBFF3CA66A4339E4EF 9D771B15279D1DC r = 133F5414F2A9BC41466D339B79376038A64D045E5B0F792A98E5A7AA87E0AD01 6419E5F8D176007D5C9C10B5FD9E2E0AB8331B195797C0358BA05ECBF24ACE59 C5F368A6C0997CC s = 3D16743AE9F00F0B1A500F738719C5582550FEB64689DA241665C4CE4F328BA0 E34A7EF527ED13BFA5889FD2D1D214C11EB17D6BC338E05A56F41CAFF1AF7B8D 574DB62EF0D0F21

With SHA-224, message = "test": k = 333C711F8C62F205F926593220233B06228285261D34026232F6F729620C6DE1 2220F282F4206D223226705608688B20B8BA86D8DFE54F07A37EC48F253283AC 33C3F5102C8CC3E r = 3048E76506C5C43D92B2E33F62B33E3111CEEB87F6C7DF7C7C01E3CDA28FA5E8 BE04B5B23AA03C0C70FEF8F723CBCEBFF0B7A52A3F5C8B84B741B4F6157E69A5 FB0524B48F31828 s = 2C99078CCFE5C82102B8D006E3703E020C46C87C75163A2CD839C885550BA5CB 501AC282D29A1C26D26773B60FBE05AAB62BFA0BA32127563D42F7669C97784C 8897C22CFB4B8FA

K = 333C711F8C62F205F926593220233B06228285261D34026232F6F729620C6DE1 2220F282F4206D223226705608688B20B8BA86D8DFE54F07A37EC48F253283AC 33C3F5102C8CC3EのR = 3048E76506C5C43D92B2E33F62B33E3111CEEB87F6C7DF7C7C01E3CDA28FA5E8 BE04B5B23AA03C0C70FEF8F723CBCEBFF0B7A52A3F5C8B84B741B4F6157E69A5 FB0524B48F31828 S = 2C99078CCFE5C82102B8D006E3703E020C46C87C75163A2CD839C885550BA5CB 501AC282D29A1C26D26773B60FBE05AAB62BFA0BA32127563D42F7669C97784C 8897C22CFB4B8FA:SHA-224、メッセージ= "テスト" と

With SHA-256, message = "test": k = 328E02CF07C7B5B6D3749D8302F1AE5BFAA8F239398459AF4A2C859C7727A812 3A7FE9BE8B228413FC8DC0E9DE16AF3F8F43005107F9989A5D97A5C4455DA895 E81336710A3FB2C r = 184BC808506E11A65D628B457FDA60952803C604CC7181B59BD25AEE1411A66D 12A777F3A0DC99E1190C58D0037807A95E5080FA1B2E5CCAA37B50D401CFFC34 17C005AEE963469 s = 27280D45F81B19334DBDB07B7E63FE8F39AC7E9AE14DE1D2A6884D2101850289 D70EE400F26ACA5E7D73F534A14568478E59D00594981ABE6A1BA18554C13EB5 E03921E4DC98333

SHA-256、メッセージ= "テスト" K = 328E02CF07C7B5B6D3749D8302F1AE5BFAA8F239398459AF4A2C859C7727A812 3A7FE9BE8B228413FC8DC0E9DE16AF3F8F43005107F9989A5D97A5C4455DA895 E81336710A3FB2C R = 184BC808506E11A65D628B457FDA60952803C604CC7181B59BD25AEE1411A66D 12A777F3A0DC99E1190C58D0037807A95E5080FA1B2E5CCAA37B50D401CFFC34 17C005AEE963469 S = 27280D45F81B19334DBDB07B7E63FE8F39AC7E9AE14DE1D2A6884D2101850289 D70EE400F26ACA5E7D73F534A14568478E59D00594981ABE6A1BA18554C13EB5 E03921E4DC98333

With SHA-384, message = "test": k = 2A77E29EAD9E811A9FDA0284C14CDFA1D9F8FA712DA59D530A06CDE54187E250 AD1D4FB5788161938B8DE049616399C5A56B0737C9564C9D4D845A4C6A7CDFCB FF0F01A82BE672E r = 319EE57912E7B0FAA1FBB145B0505849A89C6DB1EC06EA20A6A7EDE072A6268A F6FD9C809C7E422A5F33C6C3326EAD7402467DF3272A1B2726C1C20975950F0F 50D8324578F13EC s = 2CF3EA27EADD0612DD2F96F46E89AB894B01A10DF985C5FC099CFFE0EA083EB4 4BE682B08BFE405DAD5F37D0A2C59015BA41027E24B99F8F75A70B6B7385BF39 BBEA02513EB880C

K = 2A77E29EAD9E811A9FDA0284C14CDFA1D9F8FA712DA59D530A06CDE54187E250 AD1D4FB5788161938B8DE049616399C5A56B0737C9564C9D4D845A4C6A7CDFCB FF0F01A82BE672E R = 319EE57912E7B0FAA1FBB145B0505​​849A89C6DB1EC06EA20A6A7EDE072A6268A F6FD9C809C7E422A5F33C6C3326EAD7402467DF3272A1B2726C1C20975950F0F 50D8324578F13EC S = 2CF3EA27EADD0612DD2F96F46E89AB894B01A10DF985C5FC099CFFE0EA083EB4 4BE682B08BFE405DAD5F37D0A2C59015BA41027E24B99F8F75A70B6B7385BF39 BBEA02513EB880C:SHA-384、メッセージ= "テスト" と

With SHA-512, message = "test": k = 21CE6EE4A2C72C9F93BDB3B552F4A633B8C20C200F894F008643240184BE57BB 282A1645E47FBBE131E899B4C61244EFC2486D88CDBD1DD4A65EBDD837019D02 628D0DCD6ED8FB5 r = 2AA1888EAB05F7B00B6A784C4F7081D2C833D50794D9FEAF6E22B8BE728A2A90 BFCABDC803162020AA629718295A1489EE7ED0ECB8AAA197B9BDFC49D18DDD78 FC85A48F9715544 s = 0AA5371FE5CA671D6ED9665849C37F394FED85D51FEF72DA2B5F28EDFB2C6479 CA63320C19596F5E1101988E2C619E302DD05112F47E8823040CE540CD3E90DC F41DBC461744EE9

SHA-512、メッセージを= "テスト":K = 21CE6EE4A2C72C9F93BDB3B552F4A633B8C20C200F894F008643240184BE57BB 282A1645E47FBBE131E899B4C61244EFC2486D88CDBD1DD4A65EBDD837019D02 628D0DCD6ED8FB5 R = 2AA1888EAB05F7B00B6A784C4F7081D2C833D50794D9FEAF6E22B8BE728A2A90 BFCABDC803162020AA629718295A1489EE7ED0ECB8AAA197B9BDFC49D18DDD78 FC85A48F9715544 S = 0AA5371FE5CA671D6ED9665849C37F394FED85D51FEF72DA2B5F28EDFB2C6479 CA63320C19596F5E1101988E2C619E302DD05112F47E8823040CE540CD3E90DC F41DBC461744EE9

A.3. Sample Code
A.3. サンプルコード

We include here a sample implementation of deterministic DSA. It is meant for illustration purposes; for instance, this code makes no attempt at avoiding side-channel leakage of the private key. It is written in the Java programming language. The actual generation of the "random" value k is done in the computek() method. The Java virtual machine (JVM) is assumed to provide the implementation of the hash function and of HMAC.

ここでは、確定的DSAのサンプル実装を含めます。説明のためのものです。たとえば、このコードは、秘密鍵のサイドチャネル漏洩を回避しようとはしません。 Javaプログラミング言語で書かれています。 「ランダムな」値kの実際の生成は、computek()メソッドで行われます。 Java仮想マシン(JVM)は、ハッシュ関数とHMACの実装を提供すると想定されています。

  // ==================================================================
  import java.math.BigInteger;
  import javax.crypto.Mac;
  import javax.crypto.spec.SecretKeySpec;
   * Deterministic DSA signature generation.  This is a sample
   * implementation designed to illustrate how deterministic DSA
   * chooses the pseudorandom value k when signing a given message.
   * This implementation was NOT optimized or hardened against
   * side-channel leaks.
   * An instance is created with a hash function name, which must be
   * supported by the underlying Java virtual machine ("SHA-1" and
   * "SHA-256" should work everywhere).  The data to sign is input
   * through the {@code update()} methods.  The private key is set with
   * {@link #setPrivateKey}.  The signature is obtained by calling
   * {@link #sign}; alternatively, {@link #signHash} can be used to
   * sign some data that has been externally hashed.  The private key
   * MUST be set before generating the signature itself, but message
   * data can be input before setting the key.
   * Instances are NOT thread-safe.  However, once a signature has
   * been generated, the same instance can be used again for another
   * signature; {@link #setPrivateKey} need not be called again if the
   * private key has not changed.  {@link #reset} can also be called to
   * cancel previously input data.  Generating a signature with {@link
   * #sign} (not {@link #signHash}) also implicitly causes a
   * reset.
   * ------------------------------------------------------------------
   * Copyright (c) 2013 IETF Trust and the persons identified as
   * authors of the code.  All rights reserved.

* Redistribution and use in source and binary forms, with or without * modification, is permitted pursuant to, and subject to the license * terms contained in, the Simplified BSD License set forth in Section * 4.c of the IETF Trust's Legal Provisions Relating to IETF Documents * ( * * Technical remarks and questions can be addressed to: * * ------------------------------------------------------------------ */

* ソースおよびバイナリ形式での再頒布および使用は、*修正の有無にかかわらず、IETFトラストの法的規定のセクション* 4.cに記載されている*簡略化されたBSDライセンスに含まれ、それに含まれるライセンス条件に従って許可されます。 IETFドキュメント*(。 * *技術的な発言と質問は、次のアドレスに送信できます。* * -------------------------------- ---------------------------------- * /

public class DeterministicDSA {

パブリッククラスDeterministicDSA {

          private String macName;
          private MessageDigest dig;
          private Mac hmac;
          private BigInteger p, q, g, x;
          private int qlen, rlen, rolen, holen;
          private byte[] bx;
           * Create an instance, using the specified hash function.
           * The name is used to obtain from the JVM an implementation
           * of the hash function and an implementation of HMAC.
           * @param hashName   the hash function name
           * @throws IllegalArgumentException  on unsupported name
          public DeterministicDSA(String hashName)
                  try {
                          dig = MessageDigest.getInstance(hashName);
                  } catch (NoSuchAlgorithmException nsae) {
                          throw new IllegalArgumentException(nsae);
                  if (hashName.indexOf('-') < 0) {
                          macName = "Hmac" + hashName;
                  } else {
                          StringBuilder sb = new StringBuilder();
                          int n = hashName.length();
                          for (int i = 0; i < n; i ++) {
                                  char c = hashName.charAt(i);
                                  if (c != '-') {
                          macName = sb.toString();
                  try {
                          hmac = Mac.getInstance(macName);
                  } catch (NoSuchAlgorithmException nsae) {
                          throw new IllegalArgumentException(nsae);
                  holen = hmac.getMacLength();
           * Set the private key.
           * @param p   key parameter: field modulus
           * @param q   key parameter: subgroup order
           * @param g   key parameter: generator
           * @param x   private key
          public void setPrivateKey(BigInteger p, BigInteger q,
                  BigInteger g, BigInteger x)
                   * Perform some basic sanity checks.  We do not
                   * check primality of p or q because that would
                   * be too expensive.
                   * We reject keys where q is longer than 999 bits,
                   * because it would complicate signature encoding.
                   * Normal DSA keys do not have a q longer than 256
                   * bits anyway.
                  if (p == null || q == null || g == null || x == null
                          || p.signum() <= 0 || q.signum() <= 0
                          || g.signum() <= 0 || x.signum() <= 0
                          || x.compareTo(q) >= 0 || q.compareTo(p) >= 0
                          || q.bitLength() > 999
                          || g.compareTo(p) >= 0 || g.bitLength() == 1
                          || g.modPow(q, p).bitLength() != 1) {
                          throw new IllegalArgumentException(
                                  "invalid DSA private key");
                  this.p = p;
                  this.q = q;
                  this.g = g;
                  this.x = x;
                  qlen = q.bitLength();
                  if (q.signum() <= 0 || qlen < 8) {
                          throw new IllegalArgumentException(
                                  "bad group order: " + q);
                  rolen = (qlen + 7) >>> 3;
                  rlen = rolen * 8;
                   * Convert the private exponent (x) into a sequence
                   * of octets.
                  bx = int2octets(x);
          private BigInteger bits2int(byte[] in)
                  BigInteger v = new BigInteger(1, in);
                  int vlen = in.length * 8;
                  if (vlen > qlen) {
                          v = v.shiftRight(vlen - qlen);
                  return v;
          private byte[] int2octets(BigInteger v)
                  byte[] out = v.toByteArray();
                  if (out.length < rolen) {
                          byte[] out2 = new byte[rolen];
                          System.arraycopy(out, 0,
                                  out2, rolen - out.length,
                          return out2;
                  } else if (out.length > rolen) {
                          byte[] out2 = new byte[rolen];
                          System.arraycopy(out, out.length - rolen,
                                  out2, 0, rolen);
                          return out2;
                  } else {
                          return out;
          private byte[] bits2octets(byte[] in)
                  BigInteger z1 = bits2int(in);
                  BigInteger z2 = z1.subtract(q);
                  return int2octets(z2.signum() < 0 ? z1 : z2);
           * Set (or reset) the secret key used for HMAC.
           * @param K   the new secret key
          private void setHmacKey(byte[] K)
                  try {
                          hmac.init(new SecretKeySpec(K, macName));
                  } catch (InvalidKeyException ike) {
                          throw new IllegalArgumentException(ike);
           * Compute the pseudorandom k for signature generation,
           * using the process specified for deterministic DSA.
           * @param h1   the hashed message
           * @return  the pseudorandom k to use
          private BigInteger computek(byte[] h1)
                   * Convert hash value into an appropriately truncated
                   * and/or expanded sequence of octets.  The private
                   * key was already processed (into field bx[]).
                  byte[] bh = bits2octets(h1);
                   * HMAC is always used with K as key.
                   * Whenever K is updated, we reset the
                   * current HMAC key.
                  /* step b. */
                  byte[] V = new byte[holen];
                  for (int i = 0; i < holen; i ++) {
                          V[i] = 0x01;
                  /* step c. */
                  byte[] K = new byte[holen];
                  /* step d. */
                  K = hmac.doFinal();
                  /* step e. */
                  V = hmac.doFinal();
                  /* step f. */
                  K = hmac.doFinal();
                  /* step g. */
                  V = hmac.doFinal();
                  /* step h. */
                  byte[] T = new byte[rolen];
                  for (;;) {
                           * We want qlen bits, but we support only
                           * hash functions with an output length
                           * multiple of 8;acd hence, we will gather
                           * rlen bits, i.e., rolen octets.
                          int toff = 0;
                          while (toff < rolen) {
                                  V = hmac.doFinal();
                                  int cc = Math.min(V.length,
                                          T.length - toff);
                                  System.arraycopy(V, 0, T, toff, cc);
                                  toff += cc;
                          BigInteger k = bits2int(T);
                          if (k.signum() > 0 && k.compareTo(q) < 0) {
                                  return k;
                           * k is not in the proper range; update
                           * K and V, and loop.
                          K = hmac.doFinal();
                          V = hmac.doFinal();
           * Process one more byte of input data (message to sign).
           * @param in   the extra input byte
          public void update(byte in)
           * Process some extra bytes of input data (message to sign).
           * @param in   the extra input bytes
          public void update(byte[] in)
                  dig.update(in, 0, in.length);
           * Process some extra bytes of input data (message to sign).
           * @param in    the extra input buffer
           * @param off   the extra input offset
           * @param len   the extra input length (in bytes)
          public void update(byte[] in, int off, int len)
                  dig.update(in, off, len);
           * Produce the signature.  {@link #setPrivateKey} MUST have
           * been called.  The signature is computed over the data
           * that was input through the {@code update*()} methods.
           * This engine is then reset (made ready for a new
           * signature generation).
           * @return  the signature
          public byte[] sign()
                  return signHash(dig.digest());
           * Produce the signature.  {@link #setPrivateKey} MUST
           * have been called.  The signature is computed over the
           * provided hash value (data is assumed to have been hashed
           * externally).  The data that was input through the
           * {@code update*()} methods is ignored, but kept.
           * If the hash output is longer than the subgroup order
           * (the length of q, in bits, denoted 'qlen'), then the
           * provided value {@code h1} can be truncated, provided that
           * at least qlen leading bits are preserved.  In other words,
           * bit values in {@code h1} beyond the first qlen bits are
           * ignored.
           * @param h1   the hash value
           * @return  the signature
          public byte[] signHash(byte[] h1)
                  if (p == null) {
                          throw new IllegalStateException(
                                  "no private key set");
                  try {
                          BigInteger k = computek(h1);
                          BigInteger r = g.modPow(k, p).mod(q);
                          BigInteger s = k.modInverse(q).multiply(
                           * Signature encoding: ASN.1 SEQUENCE of
                           * two INTEGERs.  The conditions on q
                           * imply that the encoded version of r and
                           * s is no longer than 127 bytes for each,
                           * including DER tag and length.
                          byte[] br = r.toByteArray();
                          byte[] bs = s.toByteArray();
                          int ulen = br.length + bs.length + 4;
                          int slen = ulen + (ulen >= 128 ? 3 : 2);
                          byte[] sig = new byte[slen];
                          int i = 0;
                          sig[i ++] = 0x30;
                          if (ulen >= 128) {
                                  sig[i ++] = (byte)0x81;
                                  sig[i ++] = (byte)ulen;
                          } else {
                                  sig[i ++] = (byte)ulen;
                          sig[i ++] = 0x02;
                          sig[i ++] = (byte)br.length;
                          System.arraycopy(br, 0, sig, i, br.length);
                          i += br.length;
                          sig[i ++] = 0x02;
                          sig[i ++] = (byte)bs.length;
                          System.arraycopy(bs, 0, sig, i, bs.length);
                          return sig;
                  } catch (ArithmeticException ae) {
                          throw new IllegalArgumentException(
                                  "DSA error (bad key ?)", ae);
           * Reset this engine.  Data input through the {@code
           * update*()} methods is discarded.  The current private key,
           * if one was set, is kept unchanged.
          public void reset()
  // ==================================================================

Author's Address

Author's Address

Thomas Pornin Quebec, QC Canada