Network Working Group                                              D. Fu
Request for Comments: 4753                                    J. Solinas
Category: Informational                                              NSA
                                                            January 2007
        
Network Working Group                                              D. Fu
Request for Comments: 4753                                    J. Solinas
Category: Informational                                              NSA
                                                            January 2007
        

ECP Groups for IKE and IKEv2

IKE和IKEv2的ECP组

Status of This Memo

关于下段备忘

This memo provides information for the Internet community. It does not specify an Internet standard of any kind. Distribution of this memo is unlimited.

本备忘录为互联网社区提供信息。它没有规定任何类型的互联网标准。本备忘录的分发不受限制。

Copyright Notice

版权公告

Copyright (C) The IETF Trust (2007).

版权所有(C)IETF信托基金(2007年)。

Abstract

摘要

This document describes new Elliptic Curve Cryptography (ECC) groups for use in the Internet Key Exchange (IKE) and Internet Key Exchange version 2 (IKEv2) protocols in addition to previously defined groups. Specifically, the new curve groups are based on modular arithmetic rather than binary arithmetic. These new groups are defined to align IKE and IKEv2 with other ECC implementations and standards, particularly NIST standards. In addition, the curves defined here can provide more efficient implementation than previously defined ECC groups.

本文档描述了除先前定义的组外,在Internet密钥交换(IKE)和Internet密钥交换版本2(IKEv2)协议中使用的新椭圆曲线加密(ECC)组。具体而言,新曲线组基于模运算而不是二进制运算。这些新组的定义是使IKE和IKEv2与其他ECC实施和标准,特别是NIST标准保持一致。此外,此处定义的曲线可以提供比以前定义的ECC组更有效的实现。

Table of Contents

目录

   1. Introduction ....................................................2
   2. Requirements Terminology ........................................3
   3. Additional ECC Groups ...........................................3
      3.1. 256-bit Random ECP Group ...................................3
      3.2. 384-bit Random ECP Group ...................................4
      3.3. 521-bit Random ECP Group ...................................5
   4. Security Considerations .........................................6
   5. Alignment with Other Standards ..................................6
   6. IANA Considerations .............................................6
   7. ECP Key Exchange Data Formats ...................................7
   8. Test Vectors ....................................................7
      8.1. 256-bit Random ECP Group ...................................8
      8.2. 384-bit Random ECP Group ...................................9
      8.3. 521-bit Random ECP Group ..................................10
   9. References .....................................................12
        
   1. Introduction ....................................................2
   2. Requirements Terminology ........................................3
   3. Additional ECC Groups ...........................................3
      3.1. 256-bit Random ECP Group ...................................3
      3.2. 384-bit Random ECP Group ...................................4
      3.3. 521-bit Random ECP Group ...................................5
   4. Security Considerations .........................................6
   5. Alignment with Other Standards ..................................6
   6. IANA Considerations .............................................6
   7. ECP Key Exchange Data Formats ...................................7
   8. Test Vectors ....................................................7
      8.1. 256-bit Random ECP Group ...................................8
      8.2. 384-bit Random ECP Group ...................................9
      8.3. 521-bit Random ECP Group ..................................10
   9. References .....................................................12
        
1. Introduction
1. 介绍

This document describes default Diffie-Hellman groups for use in IKE and IKEv2 in addition to the Oakley groups included in [IKE] and the additional groups defined since [IANA-IKE]. This document assumes that the reader is familiar with the IKE protocol and the concept of Oakley Groups, as defined in RFC 2409 [IKE].

除了[IKE]中包含的Oakley组和自[IANA-IKE]以来定义的其他组之外,本文档还描述了在IKE和IKEv2中使用的默认Diffie-Hellman组。本文档假设读者熟悉RFC 2409[IKE]中定义的IKE协议和Oakley组的概念。

RFC 2409 [IKE] defines five standard Oakley Groups: three modular exponentiation groups and two elliptic curve groups over GF[2^N]. One modular exponentiation group (768 bits - Oakley Group 1) is mandatory for all implementations to support, while the other four are optional. Thirteen additional groups subsequently have been defined and assigned values by IANA. All of these additional groups are optional. Of the eighteen groups defined so far, eight are MODP groups (exponentiation groups modulo a prime), and ten are EC2N groups (elliptic curve groups over GF[2^N]). See [RFC3526] for more information on MODP groups.

RFC 2409[IKE]定义了五个标准Oakley群:GF[2^N]上的三个模幂群和两个椭圆曲线群。所有实现都必须支持一个模块化求幂组(768位-Oakley组1),而其他四个是可选的。IANA随后定义了另外13个组并为其赋值。所有这些附加组都是可选的。在迄今定义的18个群中,8个是MODP群(模素数的幂群),10个是EC2N群(GF[2^N]上的椭圆曲线群)。有关MODP组的更多信息,请参见[RFC3526]。

The purpose of this document is to expand the options available to implementers of elliptic curve groups by adding three ECP groups (elliptic curve groups modulo a prime). The reasons for adding such groups include the following.

本文档的目的是通过添加三个ECP组(模素数的椭圆曲线组),扩展椭圆曲线组实现者可用的选项。添加此类组的原因包括以下几点。

- The groups proposed afford efficiency advantages in software applications since the underlying arithmetic is integer arithmetic modulo a prime rather than binary field arithmetic. (Additional computational advantages for these groups are presented in [GMN].)

- 由于底层算法是模素数的整数算法,而不是二进制字段算法,因此所提出的组在软件应用中具有效率优势。(这些组的其他计算优势见[GMN]。)

- The groups proposed encourage alignment with other elliptic curve standards. The proposed groups are among those standardized by NIST, the Standards for Efficient Cryptography Group (SECG), ISO, and ANSI. (See Section 5 for details.)

- 提议的团体鼓励与其他椭圆曲线标准保持一致。提议的组是由NIST、高效密码标准组(SECG)、ISO和ANSI标准化的组之一。(详见第5节。)

- The groups proposed are capable of providing security consistent with the new Advanced Encryption Standard.

- 提议的小组能够提供与新的高级加密标准一致的安全性。

These groups could also be defined using the New Group Mode, but including them in this RFC will encourage interoperability of IKE implementations based upon elliptic curve groups. In addition, the availability of standardized groups will result in optimizations for a particular curve and field size and allow precomputation that could result in faster implementations.

这些组也可以使用新的组模式定义,但将它们包含在RFC中将鼓励基于椭圆曲线组的IKE实现的互操作性。此外,标准化组的可用性将导致针对特定曲线和字段大小的优化,并允许预计算,从而加快实施速度。

In summary, due to the performance advantages of elliptic curve groups in IKE implementations and the need for further alignment with other standards, this document defines three elliptic curve groups based on modular arithmetic.

综上所述,由于椭圆曲线组在IKE实现中的性能优势以及需要进一步与其他标准保持一致,本文基于模运算定义了三个椭圆曲线组。

2. Requirements Terminology
2. 需求术语

The keywords "MUST" and "SHOULD" that appear in this document are to be interpreted as described in [RFC2119].

本文件中出现的关键词“必须”和“应该”应按照[RFC2119]中所述进行解释。

3. Additional ECC Groups
3. 其他ECC组

The notation adopted in RFC 2409 [IKE] is used below to describe the new groups proposed.

下文使用RFC 2409[IKE]中采用的符号来描述提议的新组。

3.1. 256-bit Random ECP Group
3.1. 256位随机ECP组

IKE and IKEv2 implementations SHOULD support an ECP group with the following characteristics. The curve is based on the integers modulo the generalized Mersenne prime p given by

IKE和IKEv2实现应支持具有以下特征的ECP组。该曲线基于以下公式给出的广义梅森素数p的整数模:

                  p = 2^(256)-2^(224)+2^(192)+2^(96)-1
        
                  p = 2^(256)-2^(224)+2^(192)+2^(96)-1
        

The equation for the elliptic curve is:

椭圆曲线的方程为:

                  y^2 = x^3 - 3 x + b
        
                  y^2 = x^3 - 3 x + b
        

Field Size: 256

字段大小:256

Group Prime/Irreducible Polynomial: FFFFFFFF 00000001 00000000 00000000 00000000 FFFFFFFF FFFFFFFF FFFFFFFF

群素数/不可约多项式:FFFFFF00000001 00000000 00000000 FFFFFFFFFFFFFFFFFF

Group Curve b: 5AC635D8 AA3A93E7 B3EBBD55 769886BC 651D06B0 CC53B0F6 3BCE3C3E 27D2604B

组别曲线b:5AC635D8 AA3A93E7 B3EBBD55 769886BC 651D06B0 CC53B0F6 3BE3C3E 27D2604B

Group Order: FFFFFFFF 00000000 FFFFFFFF FFFFFFFF BCE6FAAD A7179E84 F3B9CAC2 FC632551

集团订单:FFFFFFFF00000000 FFFFFFFFFFFFFFFFBCE6FAAD A7179E84 F3B9CAC2 FC632551

The group was chosen verifiably at random using SHA-1 as specified in [IEEE-1363] from the seed:

使用[IEEE-1363]中规定的SHA-1从种子中随机选择该组:

C49D3608 86E70493 6A6678E1 139D26B7 819F7E90

C49D3608 86E70493 6A6678E1 139D26B7 819F7E90

The generator for this group is given by g=(gx,gy) where

该组的生成器由g=(gx,gy)给出,其中

gx: 6B17D1F2 E12C4247 F8BCE6E5 63A440F2 77037D81 2DEB33A0 F4A13945 D898C296

gx:6B17D1F2 E12C4247 F8BCE6E5 63A440F2 77037D81 2DEB33A0 F4A13945 D898C296

gy: 4FE342E2 FE1A7F9B 8EE7EB4A 7C0F9E16 2BCE3357 6B315ECE CBB64068 37BF51F5

gy:4FE342E2 FE1A7F9B 8EE7EB4A 7C0F9E16 2BCE3357 6B315ECE CBB64068 37BF51F5

3.2. 384-bit Random ECP Group
3.2. 384位随机ECP组

IKE and IKEv2 implementations SHOULD support an ECP group with the following characteristics. The curve is based on the integers modulo the generalized Mersenne prime p given by

IKE和IKEv2实现应支持具有以下特征的ECP组。该曲线基于以下公式给出的广义梅森素数p的整数模:

                  p = 2^(384)-2^(128)-2^(96)+2^(32)-1
        
                  p = 2^(384)-2^(128)-2^(96)+2^(32)-1
        

The equation for the elliptic curve is:

椭圆曲线的方程为:

                  y^2 = x^3 - 3 x + b
        
                  y^2 = x^3 - 3 x + b
        

Field Size: 384

字段大小:384

Group Prime/Irreducible Polynomial: FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFFFF 00000000 00000000 FFFFFFFF

群素数/不可约多项式:FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

Group Curve b: B3312FA7 E23EE7E4 988E056B E3F82D19 181D9C6E FE814112 0314088F 5013875A C656398D 8A2ED19D 2A85C8ED D3EC2AEF

组曲线b:B3312FA7 E23EE7E4 988E056B E3F82D19 181D9C6E FE814112 0314088F 5013875A C656398D 8A2ED19D 2A85C8ED D3EC2AEF

Group Order: FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF C7634D81 F4372DDF 581A0DB2 48B0A77A ECEC196A CCC52973

组顺序:FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81 F4372DDF 581A0DB2 48B0A77A ECEC196A CCC52973

The group was chosen verifiably at random using SHA-1 as specified in [IEEE-1363] from the seed:

使用[IEEE-1363]中规定的SHA-1从种子中随机选择该组:

A335926A A319A27A 1D00896A 6773A482 7ACDAC73

A335926A A319A27A 1D00896A 6773A482 7ACDAC73

The generator for this group is given by g=(gx,gy) where

该组的生成器由g=(gx,gy)给出,其中

gx: AA87CA22 BE8B0537 8EB1C71E F320AD74 6E1D3B62 8BA79B98 59F741E0 82542A38 5502F25D BF55296C 3A545E38 72760AB7

gx:AA87CA22 BE8B0537 8EB1C71E F320AD74 6E1D3B62 8BA79B98 59F741E0 82542A38 5502F25D BF55296C 3A545E38 72760AB7

gy: 3617DE4A 96262C6F 5D9E98BF 9292DC29 F8F41DBD 289A147C E9DA3113 B5F0B8C0 0A60B1CE 1D7E819D 7A431D7C 90EA0E5F

gy:3617DE4A 96262C6F 5D9E98BF 9292DC29 F8F41DBD 289A147C E9DA3113 B5F0B8C0 0A60B1CE 1D7E819D 7A431D7C 90EA0E5F

3.3. 521-bit Random ECP Group
3.3. 521位随机ECP组

IKE and IKEv2 implementations SHOULD support an ECP group with the following characteristics. The curve is based on the integers modulo the Mersenne prime p given by

IKE和IKEv2实现应支持具有以下特征的ECP组。该曲线基于模Mersenne素数p的整数,由

p = 2^(521)-1

p=2^(521)-1

The equation for the elliptic curve is:

椭圆曲线的方程为:

                  y^2 = x^3 - 3 x + b
        
                  y^2 = x^3 - 3 x + b
        

Field Size: 521

字段大小:521

Group Prime/Irreducible Polynomial: 01FFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFF

群素数/不可约多项式:01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

Group Curve b: 0051953E B9618E1C 9A1F929A 21A0B685 40EEA2DA 725B99B3 15F3B8B4 89918EF1 09E15619 3951EC7E 937B1652 C0BD3BB1 BF073573 DF883D2C 34F1EF45 1FD46B50 3F00

组曲线b:0051953E B9618E1C 9A1F929A 21A0B685 40EEA2DA 725B99B3 15F3B8B4 89918EF1 09E15619 3951EC7E 937B1652 C0BD3BB1 BF073573 DF883D2C 34F1EF45 1FD46B50 3F00

Group Order: 01FFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFA5186 8783BF2F 966B7FCC 0148F709 A5D03BB5 C9B8899C 47AEBB6F B71E9138 6409

集团订单:01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA5186 8783BF2F 966B7FCC 0148F709 A5D03BB5 C9B8899C 47AEBB6F B71E9138 6409

The group was chosen verifiably at random using SHA-1 as specified in [IEEE-1363] from the seed:

使用[IEEE-1363]中规定的SHA-1从种子中随机选择该组:

D09E8800 291CB853 96CC6717 393284AA A0DA64BA

D09E8800 291CB853 96CC6717 393284AA A0DA64BA

The generator for this group is given by g=(gx,gy) where

该组的生成器由g=(gx,gy)给出,其中

gx: 00C6858E 06B70404 E9CD9E3E CB662395 B4429C64 8139053F B521F828 AF606B4D 3DBAA14B 5E77EFE7 5928FE1D C127A2FF A8DE3348 B3C1856A 429BF97E 7E31C2E5 BD66

gx:00C6858E 06B70404 E9CD9E3E CB662395 B4429C64 8139053F B521F828 AF606B4D 3DBAA14B 5E77EFE7 5928FE1D C127A2FF A8DE3348 B3C1856A 429BF97E 7E31C2E5 BD66

gy: 01183929 6A789A3B C0045C8A 5FB42C7D 1BD998F5 4449579B 446817AF BD17273E 662C97EE 72995EF4 2640C550 B9013FAD 0761353C 7086A272 C24088BE 94769FD1 6650

gy:01183929 6A789A3B C0045C8A 5FB42C7D 1BD998F5 4449579B 446817AF BD17273E 662C97EE 72995EF4 2640C550 B9013FAD 0761353C 7086A272 C24088BE 94769FD1 6650

4. Security Considerations
4. 安全考虑

Since this document proposes new groups for use within IKE and IKEv2, many of the security considerations contained within [IKE] and [IKEv2] apply here as well.

由于本文档提出了在IKE和IKEv2中使用的新组,[IKE]和[IKEv2]中包含的许多安全注意事项也适用于此处。

The groups proposed in this document correspond to the symmetric key sizes 128 bits, 192 bits, and 256 bits. This allows the IKE key exchange to offer security comparable with the AES algorithms [AES].

本文档中建议的组对应于对称密钥大小128位、192位和256位。这允许IKE密钥交换提供与AES算法[AES]相当的安全性。

5. Alignment with Other Standards
5. 与其他标准保持一致

The following table summarizes the appearance of these three elliptic curve groups in other standards.

下表总结了这三个椭圆曲线组在其他标准中的外观。

                           256-bit        384-bit        521-bit
                           Random         Random         Random
   Standard                ECP Group      ECP Group      ECP Group
   -----------             ------------   ------------   ------------
        
                           256-bit        384-bit        521-bit
                           Random         Random         Random
   Standard                ECP Group      ECP Group      ECP Group
   -----------             ------------   ------------   ------------
        

NIST [DSS] P-256 P-384 P-521

NIST[DSS]P-256 P-384 P-521

ISO/IEC [ISO-15946-1] P-256

ISO/IEC[ISO-15946-1]P-256

ISO/IEC [ISO-18031] P-256 P-384 P-521

ISO/IEC[ISO-18031]P-256 P-384 P-521

ANSI [X9.62-1998] Sect. J.5.3, Example 1 ANSI [X9.62-2005] Sect. L.6.4.3 Sect. L.6.5.2 Sect. L.6.6.2

ANSI[X9.62-1998]第节。J.5.3,示例1 ANSI[X9.62-2005]第节。L.6.4.3节。L.6.5.2第节。L.6.6.2

ANSI [X9.63] Sect. J.5.4, Sect. J.5.5 Sect. J.5.6 Example 2

ANSI[X9.63]第节。J.5.4,第三节。J.5.5节。J.5.6示例2

SECG [SEC2] secp256r1 secp384r1 secp521r1

SECG[SEC2]secp256r1 secp384r1 secp521r1

See also [NIST], [ISO-14888-3], [ISO-15946-2], [ISO-15946-3], and [ISO-15946-4].

另见[NIST]、[ISO-14888-3]、[ISO-15946-2]、[ISO-15946-3]和[ISO-15946-4]。

6. IANA Considerations
6. IANA考虑

IANA has updated its registries of Diffie-Hellman groups for IKE in [IANA-IKE] and for IKEv2 in [IANA-IKEv2] to include the groups defined above.

IANA已更新了[IANA-IKE]中IKE和[IANA-IKEv2]中IKEv2的Diffie-Hellman组的注册表,以包括上述定义的组。

In [IANA-IKE], the groups appear as new entries in the list of Diffie-Hellman groups given by Group Description (attribute class 4). The descriptions are "256-bit random ECP group", "384-bit random ECP

在[IANA-IKE]中,组作为新条目出现在由组描述(属性类4)给出的Diffie-Hellman组列表中。描述为“256位随机ECP组”、“384位随机ECP组”

group", and "521-bit random ECP group". In each case, the group type (attribute class 5) has the value 2 (ECP, elliptic curve group over GF[P]).

组”和“521位随机ECP组”。在每种情况下,组类型(属性类5)的值为2(ECP,GF[P]上的椭圆曲线组)。

In [IANA-IKEv2], the groups appear as new entries in the list of IKEv2 transform type values for Transform Type 4 (Diffie-Hellman groups).

在[IANA-IKEv2]中,组作为新条目出现在变换类型4(Diffie-Hellman组)的IKEv2变换类型值列表中。

7. ECP Key Exchange Data Formats
7. 密钥交换数据格式

In an ECP key exchange, the Diffie-Hellman public value passed in a KE payload consists of two components, x and y, corresponding to the coordinates of an elliptic curve point. Each component MUST have bit length as given in the following table.

在ECP密钥交换中,在KE有效载荷中传递的Diffie-Hellman公共值由两个分量组成,x和y,对应于椭圆曲线点的坐标。每个组件必须具有下表中给出的位长度。

      Diffie-Hellman group                component bit length
      ------------------------            --------------------
        
      Diffie-Hellman group                component bit length
      ------------------------            --------------------
        

256-bit Random ECP Group 256 384-bit Random ECP Group 384 521-bit Random ECP Group 528

256位随机ECP组256 384位随机ECP组384 521位随机ECP组528

This length is enforced, if necessary, by prepending the value with zeros.

如有必要,可通过在值前面加零来强制执行此长度。

The Diffie-Hellman public value is obtained by concatenating the x and y values.

Diffie-Hellman公共值是通过连接x和y值获得的。

The format of the Diffie-Hellman shared secret value is the same as that of the Diffie-Hellman public value.

Diffie-Hellman共享秘密值的格式与Diffie-Hellman公共值的格式相同。

8. Test Vectors
8. 测试向量

The following are examples of the IKEv2 key exchange payload for each of the three groups specified in this document.

以下是本文档中指定的三个组的IKEv2密钥交换有效负载示例。

We denote by g^n the scalar multiple of the point g by the integer n; it is another point on the curve. In the literature, the scalar multiple is typically denoted ng; the notation g^n is used in order to conform to the notation used in [IKE] and [IKEv2].

我们用g^n表示点g的整数n的标量倍数;这是曲线上的另一点。在文献中,标量倍数通常表示为ng;使用符号g^n是为了符合[IKE]和[IKEv2]中使用的符号。

8.1. 256-bit Random ECP Group
8.1. 256位随机ECP组

IANA assigned the ID value 19 to this Diffie-Hellman group.

IANA将ID值19分配给这个Diffie-Hellman组。

We suppose that the initiator's Diffie-Hellman private key is

我们假设发起者的Diffie Hellman私钥是

i: C88F01F5 10D9AC3F 70A292DA A2316DE5 44E9AAB8 AFE84049 C62A9C57 862D1433

i:C88F01F5 10D9AC3F 70A292DA A2316DE5 44E9AAB8 AFE84049 C62A9C57 862D1433

Then the public key is given by g^i=(gix,giy) where

然后公钥由g^i=(gix,giy)给出,其中

gix: DAD0B653 94221CF9 B051E1FE CA5787D0 98DFE637 FC90B9EF 945D0C37 72581180

gix:DAD0B653 94221CF9 B051E1FE CA5787D0 98DFE637 FC90B9EF 945D0C37 72581180

giy: 5271A046 1CDB8252 D61F1C45 6FA3E59A B1F45B33 ACCF5F58 389E0577 B8990BB3

giy:5271A046 1CDB8252 D61F1C45 6FA3E59A B1F45B33 ACCF58 389E0577 B8990BB3

The KEi payload is as follows.

KEi有效载荷如下所示。

00000048 00130000 DAD0B653 94221CF9 B051E1FE CA5787D0 98DFE637 FC90B9EF 945D0C37 72581180 5271A046 1CDB8252 D61F1C45 6FA3E59A B1F45B33 ACCF5F58 389E0577 B8990BB3

000000 48 00130000 DAD0B653 94221CF9 B051E1FE CA5787D0 98DFE637 FC90B9EF 945D0C37 72581180 5271A046 1CDB8252 D61F1F1C45 6FA3E59A B1F45B33 ACCF58 389E0577 B8990BB3

We suppose that the response Diffie-Hellman private key is

我们假设Diffie-Hellman私钥的响应是

r: C6EF9C5D 78AE012A 011164AC B397CE20 88685D8F 06BF9BE0 B283AB46 476BEE53

r:C6EF9C5D 78AE012A 011164AC B397CE20 88685D8F 06BF9BE0 B283AB46 476BEE53

Then the public key is given by g^r=(grx,gry) where

然后公钥由g^r=(grx,gry)给出,其中

grx: D12DFB52 89C8D4F8 1208B702 70398C34 2296970A 0BCCB74C 736FC755 4494BF63

grx:D12DFB52 89C8D4F8 1208B702 70398C34 22969970A 0BCCB74C 736FC755 4494BF63

gry: 56FBF3CA 366CC23E 8157854C 13C58D6A AC23F046 ADA30F83 53E74F33 039872AB

gry:56FBF3CA 366CC23E 8157854C 13C58D6A AC23F046 ADA30F83 53E74F33 039872AB

The KEr payload is as follows.

KEr有效载荷如下所示。

00000048 00130000 D12DFB52 89C8D4F8 1208B702 70398C34 2296970A 0BCCB74C 736FC755 4494BF63 56FBF3CA 366CC23E 8157854C 13C58D6A AC23F046 ADA30F83 53E74F33 039872AB

000000 48 00130000 D12DFB52 89C8D4F8 1208B702 70398C34 22969970A 0BCCB74C 736FC755 4494BF63 56FBF3CA 366CC23E 8157854C 13C58D6A AC23F046 ADA30F83 53E74F33 039872AB

The shared secret value g^ir=(girx,giry) where

共享秘密值g^ir=(girx,giry),其中

girx: D6840F6B 42F6EDAF D13116E0 E1256520 2FEF8E9E CE7DCE03 812464D0 4B9442DE

girx:D6840F6B 42F6EDAF D13116E0 E1256520 2FEF8E9E CE7DCE03 812464D0 4B9442DE

giry: 522BDE0A F0D8585B 8DEF9C18 3B5AE38F 50235206 A8674ECB 5D98EDB2 0EB153A2

giry:522BDE0A F0D8585B 8DEF9C18 3B5AE38F 50235206 A8674ECB 5D98EDB2 0EB153A2

These are concatenated to form

这些连接在一起形成

g^ir: D6840F6B 42F6EDAF D13116E0 E1256520 2FEF8E9E CE7DCE03 812464D0 4B9442DE 522BDE0A F0D8585B 8DEF9C18 3B5AE38F 50235206 A8674ECB 5D98EDB2 0EB153A2

g^ir:D6840F6B 42F6EDAF D13116E0 E1256520 2EF8E9E CE7DCE03 812464D0 4B9442DE 522BDE0A F0D8585B 8DEF9C18 3B5AE38F 50235206 A8674ECB 5D98EDB2 0EB153A2

This is the value that is used in the formation of SKEYSEED.

这是用于形成SKEYSEED的值。

8.2. 384-bit Random ECP Group
8.2. 384位随机ECP组

IANA assigned the ID value 20 to this Diffie-Hellman group.

IANA将ID值20分配给这个Diffie-Hellman组。

We suppose that the initiator's Diffie-Hellman private key is

我们假设发起者的Diffie Hellman私钥是

i: 099F3C70 34D4A2C6 99884D73 A375A67F 7624EF7C 6B3C0F16 0647B674 14DCE655 E35B5380 41E649EE 3FAEF896 783AB194

i:099F3C70 34D4A2C6 99884D73 A375A67F 7624EF7C 6B3C0F16 0647B674 14DCE655 E35B5380 41E649EE 3FAEF896 783AB194

Then the public key is given by g^i=(gix,giy) where

然后公钥由g^i=(gix,giy)给出,其中

gix: 667842D7 D180AC2C DE6F74F3 7551F557 55C7645C 20EF73E3 1634FE72 B4C55EE6 DE3AC808 ACB4BDB4 C88732AE E95F41AA

gix:667842D7 D180AC2C DE6F74F37551F5575C7645C 20EF73E3 1634FE72 B4C55EE6 DE3AC808 ACB4BDB4 C88732AE E95F41AA

giy: 9482ED1F C0EEB9CA FC498462 5CCFC23F 65032149 E0E144AD A0241815 35A0F38E EB9FCFF3 C2C947DA E69B4C63 4573A81C

giy:9482ED1F C0EEB9CA FC498462 5CFC23F 65032149 E0E144AD A0241815 35A0F38E EB9FCFF3 C2C947DA E69B4C63 4573A81C

The KEi payload is as follows.

KEi有效载荷如下所示。

00000068 00140000 667842D7 D180AC2C DE6F74F3 7551F557 55C7645C 20EF73E3 1634FE72 B4C55EE6 DE3AC808 ACB4BDB4 C88732AE E95F41AA 9482ED1F C0EEB9CA FC498462 5CCFC23F 65032149 E0E144AD A0241815 35A0F38E EB9FCFF3 C2C947DA E69B4C63 4573A81C

000000 68 00140000 667842D7 D180AC2C DE6F74F3 7551F55C7645C 20EF73E3 1634FE72 B4C55EE6 DE3AC808 ACB4BDBB4 C88732AE E95F41AA 9482ED1F C0EEB9CA FC498462 5CFC23F 65032149 E0E144AD A0241815 35A0F38E EB9FCFF3 C2C947DA E69B4C63 4573A81C

We suppose that the response Diffie-Hellman private key is

我们假设Diffie-Hellman私钥的响应是

r: 41CB0779 B4BDB85D 47846725 FBEC3C94 30FAB46C C8DC5060 855CC9BD A0AA2942 E0308312 916B8ED2 960E4BD5 5A7448FC

r:41CB0779 B4BDB85D 47846725 FBEC3C94 30FAB46C C8DC5060 855CC9BD A0AA2942 E0308312 916B8ED2 960E4BD5 5A7448FC

Then the public key is given by g^r=(grx,gry) where

然后公钥由g^r=(grx,gry)给出,其中

grx: E558DBEF 53EECDE3 D3FCCFC1 AEA08A89 A987475D 12FD950D 83CFA417 32BC509D 0D1AC43A 0336DEF9 6FDA41D0 774A3571

grx:E558DBEF 53EECDE3 D3FCCFC1 AEA08A89 A987475D 12FD950D 83CFA417 32BC509D 0D1AC43A 0336DEF9 6FDA41D0 774A3571

gry: DCFBEC7A ACF31964 72169E83 8430367F 66EEBE3C 6E70C416 DD5F0C68 759DD1FF F83FA401 42209DFF 5EAAD96D B9E6386C

gry:DCFBEC7A ACF31964 72169E83 8430367F 66EEBE3C 6E70C416 DD5F0C68 759DD1F F83FA401 42209DFF 5EAAD96D B9E6386C

The KEr payload is as follows.

KEr有效载荷如下所示。

00000068 00140000 E558DBEF 53EECDE3 D3FCCFC1 AEA08A89 A987475D 12FD950D 83CFA417 32BC509D 0D1AC43A 0336DEF9 6FDA41D0 774A3571 DCFBEC7A ACF31964 72169E83 8430367F 66EEBE3C 6E70C416 DD5F0C68 759DD1FF F83FA401 42209DFF 5EAAD96D B9E6386C

000000 68 00140000 E558DBEF 53EECDE3 D3FCCFC1 AEA08A89 A987475D 12FD950D 83CFA417 32BC509D 0D1AC43A 0336DEF9 6FDA41D0 774A3571 DCFBEC7A ACF31964 72169E83 8430367F 66EEBE3C 6E70C416 DD5F0C68 759DD1F F83FA401 42209DFF 5EAAD96D B9E6386C

The shared secret value g^ir=(girx,giry) where

共享秘密值g^ir=(girx,giry),其中

girx: 11187331 C279962D 93D60424 3FD592CB 9D0A926F 422E4718 7521287E 7156C5C4 D6031355 69B9E9D0 9CF5D4A2 70F59746

girx:11187331 C279962D 93D60424 3FD592CB 9D0A926F 422E4718 7521287E 7156C5C4 D6031355 69B9E9D0 9CF5D4A2 70F59746

giry: A2A9F38E F5CAFBE2 347CF7EC 24BDD5E6 24BC93BF A82771F4 0D1B65D0 6256A852 C983135D 4669F879 2F2C1D55 718AFBB4

giry:A2A9F38E F5CAFBE2347CF7EC 24BDD5E6 24BC93BF A82771F4 0D1B65D0 6256A852 C983135D 4669F879 2F2C1D55 718AFBB4

These are concatenated to form

这些连接在一起形成

g^ir: 11187331 C279962D 93D60424 3FD592CB 9D0A926F 422E4718 7521287E 7156C5C4 D6031355 69B9E9D0 9CF5D4A2 70F59746 A2A9F38E F5CAFBE2 347CF7EC 24BDD5E6 24BC93BF A82771F4 0D1B65D0 6256A852 C983135D 4669F879 2F2C1D55 718AFBB4

g^ir:11187331 C279962D 93D60424 3FD592CB 9D0A926F 422E4718 7521287E 7156C5C4 D6031355 69B9E9D0 9CF5D4A2 70F59746 A2A9F38E F5CAFBE2 347CF7EC 24BDD5E6 24BC93BF A82771F4 0D1B65D0 6256A6852 C983135D 4669F879 2F2C1D55 718AFBB4

This is the value that is used in the formation of SKEYSEED.

这是用于形成SKEYSEED的值。

8.3. 521-bit Random ECP Group
8.3. 521位随机ECP组

IANA assigned the ID value 21 to this Diffie-Hellman group.

IANA将ID值21分配给这个Diffie-Hellman组。

We suppose that the initiator's Diffie-Hellman private key is

我们假设发起者的Diffie Hellman私钥是

i: 0037ADE9 319A89F4 DABDB3EF 411AACCC A5123C61 ACAB57B5 393DCE47 608172A0 95AA85A3 0FE1C295 2C6771D9 37BA9777 F5957B26 39BAB072 462F68C2 7A57382D 4A52

i:0037ADE9 319A89F4 DABDB3EF 411ACCC A5123C61 ACAB57B5 393DCE47 608172A0 95AA85A3 0FE1C295 2C6771D9 37BA9777 F5957B26 39BAB072 462F68C2 7A57382D 4A52

Then the public key is given by g^i=(gix,giy) where

然后公钥由g^i=(gix,giy)给出,其中

gix: 0015417E 84DBF28C 0AD3C278 713349DC 7DF153C8 97A1891B D98BAB43 57C9ECBE E1E3BF42 E00B8E38 0AEAE57C 2D107564 94188594 2AF5A7F4 601723C4 195D176C ED3E

gix:0015417E 84DBF28C 0AD3C278 713349DC 7DF153C8 97A1891B D98BAB43 57C9ECBE E1E3BF42 E00B8E38 0AEAE57C 2D107564 94188594 2AF5A7F4 601723C4 195D176C ED3E

giy: 017CAE20 B6641D2E EB695786 D8C94614 6239D099 E18E1D5A 514C739D 7CB4A10A D8A78801 5AC405D7 799DC75E 7B7D5B6C F2261A6A 7F150743 8BF01BEB 6CA3926F 9582

giy:017CAE20 B6641D2E EB695786 D8C94614 6239D099 E18E1D5A 514C739D 7CB4A10A D8A78801 5AC405D7 799DC75E 7B7D5B6C F2261A6A 7F150743 8BF01BEB 6CA3926F 9582

The KEi payload is as follows.

KEi有效载荷如下所示。

0000008C 00150000 0015417E 84DBF28C 0AD3C278 713349DC 7DF153C8 97A1891B D98BAB43 57C9ECBE E1E3BF42 E00B8E38 0AEAE57C 2D107564 94188594 2AF5A7F4 601723C4 195D176C ED3E017C AE20B664 1D2EEB69 5786D8C9 46146239 D099E18E 1D5A514C 739D7CB4 A10AD8A7 88015AC4 05D7799D C75E7B7D 5B6CF226 1A6A7F15 07438BF0 1BEB6CA3 926F9582

000000 8C 00150000 0015417E 84DBF28C 0AD3C278 713349DC 7DF153C8 97A1891B D98BAB43 57C9ECBE E1E3BF42 E00B8E38 0AEAE57C 2D107564 94188594 2AF5A7F4 601723C4 195D176C ED3E017C AE20B664 1DEB69 5786D8C9 46146239 D099E18E 1D5A514C 739D7CB4 A10AD8A7 88015AC4 05D7799D C75E7B7B7D 5CF226 1A07438BF926

We suppose that the response Diffie-Hellman private key is

我们假设Diffie-Hellman私钥的响应是

r: 0145BA99 A847AF43 793FDD0E 872E7CDF A16BE30F DC780F97 BCCC3F07 8380201E 9C677D60 0B343757 A3BDBF2A 3163E4C2 F869CCA7 458AA4A4 EFFC311F 5CB15168 5EB9

r:0145BA99 A847AF43 793FDD0E 872E7CDF A16BE30F DC780F97 BCCC3F07 8380201E 9C677D60 0B343757 A3BDBF2A 3163E4C2 F869CCA7 458AA4A4有效C311F 5CB15168 5EB9

Then the public key is given by g^r=(grx,gry) where

然后公钥由g^r=(grx,gry)给出,其中

grx: 00D0B397 5AC4B799 F5BEA16D 5E13E9AF 971D5E9B 984C9F39 728B5E57 39735A21 9B97C356 436ADC6E 95BB0352 F6BE64A6 C2912D4E F2D0433C ED2B6171 640012D9 460F

grx:00D0B397 5AC4B799 F5BEA16D 5E13E9AF 971D5E9B 984C9F39 728B5E57 39735A21 9B97C356 436ADC6E 95BB0352 F6BE64A6 C2912D4E F2D0433C ED2B6171 640012D9 460F

gry: 015C6822 6383956E 3BD066E7 97B623C2 7CE0EAC2 F551A10C 2C724D98 52077B87 220B6536 C5C408A1 D2AEBB8E 86D678AE 49CB5709 1F473229 6579AB44 FCD17F0F C56A

gry:015C6826383956E 3BD066E7 97B623C2 7CE0EAC2 F551A0C 2C724D98 52077B87 220B6536 C5C408A1 D2AEBB8E 86D678AE 49CB5709 1F473229 6579AB44 FCD17F0F C56A

The KEr payload is as follows.

KEr有效载荷如下所示。

0000008c 00150000 00D0B397 5AC4B799 F5BEA16D 5E13E9AF 971D5E9B 984C9F39 728B5E57 39735A21 9B97C356 436ADC6E 95BB0352 F6BE64A6 C2912D4E F2D0433C ED2B6171 640012D9 460F015C 68226383 956E3BD0 66E797B6 23C27CE0 EAC2F551 A10C2C72 4D985207 7B87220B 6536C5C4 08A1D2AE BB8E86D6 78AE49CB 57091F47 32296579 AB44FCD1 7F0FC56A

000000 8C 00150000 00D0B397 5AC4B799 F5BEA16D 5E13E9AF 971D5E9B 984C9F39 728B5E57 39735A21 9B97C356 436ADC6E 95BB0352 F6BE64A6 C2912D4E F2D0433C ED2B6171 640012D9 460F015C 68226383 956E3BD0 66E797B6 23C27CE0 EAC22F551 A10C2C72 4D985207 7B87220B 6536C508A1D2AE BBE86D6 78AECB 570915F477FC447A

The shared secret value g^ir=(girx,giry) where

共享秘密值g^ir=(girx,giry),其中

girx: 01144C7D 79AE6956 BC8EDB8E 7C787C45 21CB086F A64407F9 7894E5E6 B2D79B04 D1427E73 CA4BAA24 0A347868 59810C06 B3C715A3 A8CC3151 F2BEE417 996D19F3 DDEA

girx:01144C7D 79AE6956 BC8EDB8E 7C787C45 21CB086F A64407F9 7894E5E6 B2D79B04 D1427E73 CA4BAA24 0A347868 59810C06 B3C715A3 A8CC3151 F2417 996D19F3 DDEA

giry: 01B901E6 B17DB294 7AC017D8 53EF1C16 74E5CFE5 9CDA18D0 78E05D1B 5242ADAA 9FFC3C63 EA05EDB1 E13CE5B3 A8E50C3E B622E8DA 1B38E0BD D1F88569 D6C99BAF FA43

giry:01B901E6 B17DB294 7AC017D8 53EF1C16 74E5CFE5 9CDA18D0 78E05D1B 5242ADA 9FFC3C63 EA05EDB1 E13CE5B3 A8E50C3E B622E8DA 1B38E0BD D1F88569 D6C99BAF FA43

These are concatenated to form

这些连接在一起形成

g^ir: 01144C7D 79AE6956 BC8EDB8E 7C787C45 21CB086F A64407F9 7894E5E6 B2D79B04 D1427E73 CA4BAA24 0A347868 59810C06 B3C715A3 A8CC3151 F2BEE417 996D19F3 DDEA01B9 01E6B17D B2947AC0 17D853EF 1C1674E5 CFE59CDA 18D078E0 5D1B5242 ADAA9FFC 3C63EA05 EDB1E13C E5B3A8E5 0C3EB622 E8DA1B38 E0BDD1F8 8569D6C9 9BAFFA43

g^ir:01144C7D 79AE6956 BC8EDB8E 7C787C45 21CB086F A64407F9 7894E6 B2D79B04 D1427E73 CA4BAA24 0A347868 59810C06 B3C715A3 A8CC3151 F2BEE417 996D19F3 DDEA01E6B17D B2947AC0 17D853EF 1C1674E5 CFE59CDA 18D078E0 5D1B542 ADAA9FFC 3C63EA05 EDB13C 8E538E562EB628 B2947AC0

This is the value that is used in the formation of SKEYSEED.

这是用于形成SKEYSEED的值。

9. References
9. 工具书类
9.1. Normative References
9.1. 规范性引用文件
   [IANA-IKE]     Internet Assigned Numbers Authority, Internet Key
                  Exchange (IKE) Attributes.
                  (http://www.iana.org/assignments/ipsec-registry)
        
   [IANA-IKE]     Internet Assigned Numbers Authority, Internet Key
                  Exchange (IKE) Attributes.
                  (http://www.iana.org/assignments/ipsec-registry)
        
   [IANA-IKEv2]   IKEv2 Parameters.
                  (http://www.iana.org/assignments/ikev2-parameters)
        
   [IANA-IKEv2]   IKEv2 Parameters.
                  (http://www.iana.org/assignments/ikev2-parameters)
        

[IKE] Harkins, D. and D. Carrel, "The Internet Key Exchange (IKE)", RFC 2409, November 1998.

[IKE]Harkins,D.和D.Carrel,“互联网密钥交换(IKE)”,RFC 2409,1998年11月。

[IKEv2] Kaufman, C., "Internet Key Exchange (IKEv2) Protocol", RFC 4306, December 2005.

[IKEv2]Kaufman,C.,“互联网密钥交换(IKEv2)协议”,RFC4306,2005年12月。

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

[RFC2119]Bradner,S.,“RFC中用于表示需求水平的关键词”,BCP 14,RFC 2119,1997年3月。

9.2. Informative References
9.2. 资料性引用
   [AES]          U.S. Department of Commerce/National Institute of
                  Standards and Technology, Advanced Encryption Standard
                  (AES), FIPS PUB 197, November 2001.
                  (http://csrc.nist.gov/publications/fips/index.html)
        
   [AES]          U.S. Department of Commerce/National Institute of
                  Standards and Technology, Advanced Encryption Standard
                  (AES), FIPS PUB 197, November 2001.
                  (http://csrc.nist.gov/publications/fips/index.html)
        
   [DSS]          U.S. Department of Commerce/National Institute of
                  Standards and Technology, Digital Signature Standard
                  (DSS), FIPS PUB 186-2, January 2000.
                  (http://csrc.nist.gov/publications/fips/index.html)
        
   [DSS]          U.S. Department of Commerce/National Institute of
                  Standards and Technology, Digital Signature Standard
                  (DSS), FIPS PUB 186-2, January 2000.
                  (http://csrc.nist.gov/publications/fips/index.html)
        

[GMN] J. Solinas, Generalized Mersenne Numbers, Combinatorics and Optimization Research Report 99-39, 1999. (http://www.cacr.math.uwaterloo.ca/)

[GMN]J.Solinas,广义梅森数,组合学和优化研究报告99-391999。(http://www.cacr.math.uwaterloo.ca/)

   [IEEE-1363]    Institute of Electrical and Electronics Engineers.
                  IEEE 1363-2000, Standard for Public Key Cryptography.
                  (http://grouper.ieee.org/groups/1363/index.html)
        
   [IEEE-1363]    Institute of Electrical and Electronics Engineers.
                  IEEE 1363-2000, Standard for Public Key Cryptography.
                  (http://grouper.ieee.org/groups/1363/index.html)
        

[ISO-14888-3] International Organization for Standardization and International Electrotechnical Commission, ISO/IEC 14888-3:2006, Information Technology: Security Techniques: Digital Signatures with Appendix: Part 3 - Discrete Logarithm Based Mechanisms.

[ISO-14888-3]国际标准化组织和国际电工委员会,ISO/IEC 14888-3:2006,信息技术:安全技术:带附录的数字签名:第3部分-基于离散对数的机制。

[ISO-15946-1] International Organization for Standardization and International Electrotechnical Commission, ISO/IEC 15946-1: 2002-12-01, Information Technology: Security Techniques: Cryptographic Techniques based on Elliptic Curves: Part 1 - General.

[ISO-15946-1]国际标准化组织和国际电工委员会,ISO/IEC 15946-1:2002-12-01,信息技术:安全技术:基于椭圆曲线的加密技术:第1部分-概述。

[ISO-15946-2] International Organization for Standardization and International Electrotechnical Commission, ISO/IEC 15946-2: 2002-12-01, Information Technology: Security Techniques: Cryptographic Techniques based on Elliptic Curves: Part 2 - Digital Signatures.

[ISO-15946-2]国际标准化组织和国际电工委员会,ISO/IEC 15946-2:2002-12-01,信息技术:安全技术:基于椭圆曲线的加密技术:第2部分-数字签名。

[ISO-15946-3] International Organization for Standardization and International Electrotechnical Commission, ISO/IEC 15946-3: 2002-12-01, Information Technology: Security Techniques: Cryptographic Techniques based on Elliptic Curves: Part 3 - Key Establishment.

[ISO-15946-3]国际标准化组织和国际电工委员会,ISO/IEC 15946-3:2002-12-01,信息技术:安全技术:基于椭圆曲线的加密技术:第3部分-密钥建立。

[ISO-15946-4] International Organization for Standardization and International Electrotechnical Commission, ISO/IEC 15946-4: 2004-10-01, Information Technology: Security Techniques: Cryptographic Techniques based on Elliptic Curves: Part 4 - Digital Signatures giving Message Recovery.

[ISO-15946-4]国际标准化组织和国际电工委员会,ISO/IEC 15946-4:2004-10-01,信息技术:安全技术:基于椭圆曲线的加密技术:第4部分-提供消息恢复的数字签名。

[ISO-18031] International Organization for Standardization and International Electrotechnical Commission, ISO/IEC 18031:2005, Information Technology: Security Techniques: Random Bit Generation.

[ISO-18031]国际标准化组织和国际电工委员会,ISO/IEC 18031:2005,信息技术:安全技术:随机位生成。

[NIST] U.S. Department of Commerce/National Institute of Standards and Technology. Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography, NIST Special Publication Publication 800-56A, March 2006. (http://csrc.nist.gov/CryptoToolkit/KeyMgmt.html)

[NIST]美国商务部/国家标准与技术研究所。关于使用离散对数加密的成对密钥建立方案的建议,NIST特别出版物800-56A,2006年3月。(http://csrc.nist.gov/CryptoToolkit/KeyMgmt.html)

[RFC3526] Kivinen, T. and M. Kojo, "More Modular Exponential (MODP) Diffie-Hellman groups for Internet Key Exchange (IKE)", RFC 3526, May 2003.

[RFC3526]Kivinen,T.和M.Kojo,“互联网密钥交换(IKE)的更多模指数(MODP)Diffie-Hellman群”,RFC 3526,2003年5月。

[SEC2] Standards for Efficient Cryptography Group. SEC 2 - Recommended Elliptic Curve Domain Parameters, v. 1.0, 2000. (http://www.secg.org)

[SEC2]高效加密组标准。第2节-建议的椭圆曲线域参数,v。1.0, 2000. (http://www.secg.org)

[X9.62-1998] American National Standards Institute, X9.62-1998: Public Key Cryptography for the Financial Services Industry: The Elliptic Curve Digital Signature Algorithm. January 1999.

[X9.62-1998]美国国家标准协会,X9.62-1998:金融服务业的公钥加密:椭圆曲线数字签名算法。1999年1月。

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

[X9.62-2005]美国国家标准协会,X9.62:2005:金融服务业的公钥加密:椭圆曲线数字签名算法(ECDSA)。

[X9.63] American National Standards Institute. X9.63-2001, Public Key Cryptography for the Financial Services Industry: Key Agreement and Key Transport using Elliptic Curve Cryptography. November 2001.

[X9.63]美国国家标准协会。X9.63-2001,金融服务业的公钥加密:使用椭圆曲线加密的密钥协议和密钥传输。2001年11月。

Authors' Addresses

作者地址

David E. Fu National Information Assurance Research Laboratory National Security Agency

国家安全局国家信息保障研究实验室

   EMail: defu@orion.ncsc.mil
        
   EMail: defu@orion.ncsc.mil
        

Jerome A. Solinas National Information Assurance Research Laboratory National Security Agency

Jerome A.Solinas国家信息保障研究实验室国家安全局

   EMail: jasolin@orion.ncsc.mil
        
   EMail: jasolin@orion.ncsc.mil
        

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确认

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