Internet Engineering Task Force (IETF) J. Merkle
Request for Comments: 7027 secunet Security Networks
Updates: 4492 M. Lochter
Category: Informational BSI
ISSN: 2070-1721 October 2013
Internet Engineering Task Force (IETF) J. Merkle
Request for Comments: 7027 secunet Security Networks
Updates: 4492 M. Lochter
Category: Informational BSI
ISSN: 2070-1721 October 2013
Elliptic Curve Cryptography (ECC) Brainpool Curves for Transport Layer Security (TLS)
用于传输层安全（TLS）的椭圆曲线密码（ECC）智能池曲线
Abstract
摘要
This document specifies the use of several Elliptic Curve Cryptography (ECC) Brainpool curves for authentication and key exchange in the Transport Layer Security (TLS) protocol.
本文档规定了在传输层安全（TLS）协议中使用几种椭圆曲线加密（ECC）脑池曲线进行身份验证和密钥交换。
Status of This Memo
关于下段备忘
This document is not an Internet Standards Track specification; it is published for informational purposes.
本文件不是互联网标准跟踪规范；它是为了提供信息而发布的。
This document is a product of the Internet Engineering Task Force (IETF). It represents the consensus of the IETF community. It has received public review and has been approved for publication by the Internet Engineering Steering Group (IESG). Not all documents approved by the IESG are a candidate for any level of Internet Standard; see Section 2 of RFC 5741.
本文件是互联网工程任务组（IETF）的产品。它代表了IETF社区的共识。它已经接受了公众审查，并已被互联网工程指导小组（IESG）批准出版。并非IESG批准的所有文件都适用于任何级别的互联网标准；见RFC 5741第2节。
Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at http://www.rfc-editor.org/info/rfc7027.
有关本文件当前状态、任何勘误表以及如何提供反馈的信息，请访问http://www.rfc-editor.org/info/rfc7027.
Copyright Notice
版权公告
Copyright (c) 2013 IETF Trust and the persons identified as the document authors. All rights reserved.
版权所有（c）2013 IETF信托基金和确定为文件作者的人员。版权所有。
This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) 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. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License.
本文件受BCP 78和IETF信托有关IETF文件的法律规定的约束(http://trustee.ietf.org/license-info)自本文件出版之日起生效。请仔细阅读这些文件，因为它们描述了您对本文件的权利和限制。从本文件中提取的代码组件必须包括信托法律条款第4.e节中所述的简化BSD许可证文本，并提供简化BSD许可证中所述的无担保。
Table of Contents
目录
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Brainpool NamedCurve Types . . . . . . . . . . . . . . . . . . 2
3. IANA Considerations . . . . . . . . . . . . . . . . . . . . . . 3
4. Security Considerations . . . . . . . . . . . . . . . . . . . . 3
5. References . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5.1. Normative References . . . . . . . . . . . . . . . . . . . 4
5.2. Informative References . . . . . . . . . . . . . . . . . . 4
Appendix A. Test Vectors . . . . . . . . . . . . . . . . . . . . . 6
A.1. 256-Bit Curve . . . . . . . . . . . . . . . . . . . . . . . 7
A.2. 384-Bit Curve . . . . . . . . . . . . . . . . . . . . . . . 8
A.3. 512-Bit Curve . . . . . . . . . . . . . . . . . . . . . . . 9
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Brainpool NamedCurve Types . . . . . . . . . . . . . . . . . . 2
3. IANA Considerations . . . . . . . . . . . . . . . . . . . . . . 3
4. Security Considerations . . . . . . . . . . . . . . . . . . . . 3
5. References . . . . . . . . . . . . . . . . . . . . . . . . . . 4
5.1. Normative References . . . . . . . . . . . . . . . . . . . 4
5.2. Informative References . . . . . . . . . . . . . . . . . . 4
Appendix A. Test Vectors . . . . . . . . . . . . . . . . . . . . . 6
A.1. 256-Bit Curve . . . . . . . . . . . . . . . . . . . . . . . 7
A.2. 384-Bit Curve . . . . . . . . . . . . . . . . . . . . . . . 8
A.3. 512-Bit Curve . . . . . . . . . . . . . . . . . . . . . . . 9
[RFC5639] specifies a new set of elliptic curve groups over finite prime fields for use in cryptographic applications. These groups, denoted as ECC Brainpool curves, were generated in a verifiably pseudo-random way and comply with the security requirements of relevant standards from ISO [ISO1] [ISO2], ANSI [ANSI1], NIST [FIPS], and SecG [SEC2].
[RFC5639]指定有限素数域上的一组新椭圆曲线组，用于加密应用程序。这些组表示为ECC脑池曲线，以可验证的伪随机方式生成，并符合ISO[ISO1][ISO2]、ANSI[ANSI1]、NIST[FIPS]和SecG[SEC2]相关标准的安全要求。
[RFC4492] defines the usage of elliptic curves for authentication and key agreement in TLS 1.0 and TLS 1.1; these mechanisms may also be used with TLS 1.2 [RFC5246]. While the ASN.1 object identifiers defined in [RFC5639] already allow usage of the ECC Brainpool curves for TLS (client or server) authentication through reference in X.509 certificates according to [RFC3279] and [RFC5480], their negotiation for key exchange according to [RFC4492] requires the definition and assignment of additional NamedCurve IDs. This document specifies such values for three curves from [RFC5639].
[RFC4492]定义了在TLS 1.0和TLS 1.1中使用椭圆曲线进行身份验证和密钥协商；这些机制也可用于TLS 1.2[RFC5246]。虽然[RFC5639]中定义的ASN.1对象标识符已经允许通过参考[RFC3279]和[RFC5480]中的X.509证书使用ECC脑池曲线进行TLS（客户端或服务器）身份验证，但它们的密钥交换协商符合[RFC4492]需要定义和分配其他NamedCurve ID。本文件规定了[RFC5639]中三条曲线的此类值。
According to [RFC4492], the name space NamedCurve is used for the negotiation of elliptic curve groups for key exchange during a handshake starting a new TLS session. This document adds new NamedCurve types to three elliptic curves defined in [RFC5639] as follows:
根据[RFC4492]，名称空间NamedCurve用于在握手启动新TLS会话期间协商椭圆曲线组以进行密钥交换。本文档为[RFC5639]中定义的三条椭圆曲线添加了新的命名曲线类型，如下所示：
enum {
brainpoolP256r1(26),
brainpoolP384r1(27),
brainpoolP512r1(28)
} NamedCurve;
enum {
brainpoolP256r1(26),
brainpoolP384r1(27),
brainpoolP512r1(28)
} NamedCurve;
These curves are suitable for use with Datagram TLS [RFC6347].
这些曲线适用于数据报TLS[RFC6347]。
Test vectors for a Diffie-Hellman key exchange using these elliptic curves are provided in Appendix A.
附录a中提供了使用这些椭圆曲线的Diffie-Hellman密钥交换的测试向量。
IANA has assigned numbers for the ECC Brainpool curves listed in Section 2 in the "EC Named Curve" [IANA-TLS] registry of the "Transport Layer Security (TLS) Parameters" registry as follows:
IANA为“传输层安全（TLS）参数”注册表的“EC命名曲线”[IANA-TLS]注册表第2节中列出的ECC脑池曲线分配了编号，如下所示：
+-------+-----------------+---------+-----------+
| Value | Description | DTLS-OK | Reference |
+-------+-----------------+---------+-----------+
| 26 | brainpoolP256r1 | Y | RFC 7027 |
| 27 | brainpoolP384r1 | Y | RFC 7027 |
| 28 | brainpoolP512r1 | Y | RFC 7027 |
+-------+-----------------+---------+-----------+
+-------+-----------------+---------+-----------+
| Value | Description | DTLS-OK | Reference |
+-------+-----------------+---------+-----------+
| 26 | brainpoolP256r1 | Y | RFC 7027 |
| 27 | brainpoolP384r1 | Y | RFC 7027 |
| 28 | brainpoolP512r1 | Y | RFC 7027 |
+-------+-----------------+---------+-----------+
Table 1
表1
The security considerations of [RFC5246] apply to the ECC Brainpool curves described in this document.
[RFC5246]的安全注意事项适用于本文档中描述的ECC脑池曲线。
The confidentiality, authenticity, and integrity of the TLS communication is limited by the weakest cryptographic primitive applied. In order to achieve a maximum security level when using one of the elliptic curves from Table 1 for authentication and/or key exchange in TLS, the key derivation function; the algorithms and key lengths of symmetric encryption; and message authentication (as well as the algorithm, bit length, and hash function used for signature generation) should be chosen according to the recommendations of [NIST800-57] and [RFC5639]. Furthermore, the private Diffie-Hellman keys should be selected with the same bit length as the order of the group generated by the base point G and with approximately maximum entropy.
TLS通信的机密性、真实性和完整性受到应用的最薄弱的加密原语的限制。为了在TLS中使用表1中的一条椭圆曲线进行身份验证和/或密钥交换时达到最大安全级别，密钥派生函数；对称加密的算法和密钥长度；应根据[NIST800-57]和[RFC5639]的建议选择消息身份验证（以及用于生成签名的算法、位长度和哈希函数）。此外，私有Diffie-Hellman密钥的选择应具有与基点G生成的组的顺序相同的比特长度，并且具有近似最大熵。
Implementations of elliptic curve cryptography for TLS may be
susceptible to side-channel attacks. Particular care should be taken
for implementations that internally transform curve points to points
on the corresponding "twisted curve", using the map (x',y') = (x*Z^2,
y*Z^3) with the coefficient Z specified for that curve in [RFC5639],
in order to take advantage of an efficient arithmetic based on the
twisted curve's special parameters (A = -3). Although the twisted
curve itself offers the same level of security as the corresponding
random curve (through mathematical equivalence), an arithmetic based
on small curve parameters may be harder to protect against side-
Implementations of elliptic curve cryptography for TLS may be
susceptible to side-channel attacks. Particular care should be taken
for implementations that internally transform curve points to points
on the corresponding "twisted curve", using the map (x',y') = (x*Z^2,
y*Z^3) with the coefficient Z specified for that curve in [RFC5639],
in order to take advantage of an efficient arithmetic based on the
twisted curve's special parameters (A = -3). Although the twisted
curve itself offers the same level of security as the corresponding
random curve (through mathematical equivalence), an arithmetic based
on small curve parameters may be harder to protect against side-
channel attacks. General guidance on resistance of elliptic curve cryptography implementations against side-channel-attacks is given in [BSI1] and [HMV].
通道攻击。[BSI1]和[HMV]中给出了关于椭圆曲线密码实现抵抗旁道攻击的一般指南。
[IANA-TLS] Internet Assigned Numbers Authority, "Transport Layer Security (TLS) Parameters", <http://www.iana.org/assignments/tls-parameters>.
[IANA-TLS]互联网分配号码管理局，“传输层安全（TLS）参数”<http://www.iana.org/assignments/tls-parameters>.
[RFC4492] Blake-Wilson, S., Bolyard, N., Gupta, V., Hawk, C., and B. Moeller, "Elliptic Curve Cryptography (ECC) Cipher Suites for Transport Layer Security (TLS)", RFC 4492, May 2006.
[RFC4492]Blake Wilson，S.，Bolyard，N.，Gupta，V.，Hawk，C.，和B.Moeller，“用于传输层安全（TLS）的椭圆曲线密码（ECC）密码套件”，RFC 4492，2006年5月。
[RFC5246] Dierks, T. and E. Rescorla, "The Transport Layer Security (TLS) Protocol Version 1.2", RFC 5246, August 2008.
[RFC5246]Dierks，T.和E.Rescorla，“传输层安全（TLS）协议版本1.2”，RFC 5246，2008年8月。
[RFC5639] Lochter, M. and J. Merkle, "Elliptic Curve Cryptography (ECC) Brainpool Standard Curves and Curve Generation", RFC 5639, March 2010.
[RFC5639]Lochter，M.和J.Merkle，“椭圆曲线加密（ECC）大脑池标准曲线和曲线生成”，RFC 56392010年3月。
[RFC6347] Rescorla, E. and N. Modadugu, "Datagram Transport Layer Security Version 1.2", RFC 6347, January 2012.
[RFC6347]Rescorla，E.和N.Modadugu，“数据报传输层安全版本1.2”，RFC 6347，2012年1月。
[ANSI1] American National Standards Institute, "Public Key Cryptography For The Financial Services Industry: The Elliptic Curve Digital Signature Algorithm (ECDSA)", ANSI X9.62, 2005.
[ANSI1]美国国家标准协会，“金融服务业的公钥加密：椭圆曲线数字签名算法（ECDSA）”，ANSI X9.622005。
[BSI1] Bundesamt fuer Sicherheit in der Informationstechnik, "Minimum Requirements for Evaluating Side-Channel Attack Resistance of Elliptic Curve Implementations", July 2011.
[BSI1]信息技术领域的Bundesamt fuer-Sicherheit，“评估椭圆曲线实现的侧信道抗攻击能力的最低要求”，2011年7月。
[FIPS] National Institute of Standards and Technology, "Digital Signature Standard (DSS)", FIPS PUB 186-2, December 1998.
[FIPS]国家标准与技术研究所，“数字签名标准（DSS）”，FIPS PUB 186-2，1998年12月。
[HMV] Hankerson, D., Menezes, A., and S. Vanstone, "Guide to Elliptic Curve Cryptography", Springer Verlag, 2004.
[HMV]Hankerson，D.，Menezes，A.，和S.Vanstone，“椭圆曲线密码术指南”，Springer Verlag，2004年。
[ISO1] International Organization for Standardization, "Information Technology - Security Techniques - Digital Signatures with Appendix - Part 3: Discrete Logarithm Based Mechanisms", ISO/IEC 14888-3, 2006.
[ISO1]国际标准化组织，“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/IEC 14888-3，2006年。
[ISO2] International Organization for Standardization, "Information Technology - Security Techniques - Cryptographic Techniques Based on Elliptic Curves - Part 2: Digital signatures", ISO/IEC 15946-2, 2002.
[ISO2]国际标准化组织，“信息技术-安全技术-基于椭圆曲线的密码技术-第2部分：数字签名”，ISO/IEC 15946-22002。
[NIST800-57] National Institute of Standards and Technology, "Recommendation for Key Management - Part 1: General (Revised)", NIST Special Publication 800-57, March 2007.
[NIST 800-57]国家标准与技术研究所，“关键管理建议-第1部分：总则（修订）”，NIST特别出版物800-57，2007年3月。
[RFC3279] Bassham, L., Polk, W., and R. Housley, "Algorithms and Identifiers for the Internet X.509 Public Key Infrastructure Certificate and Certificate Revocation List (CRL) Profile", RFC 3279, April 2002.
[RFC3279]Bassham，L.，Polk，W.，和R.Housley，“互联网X.509公钥基础设施证书和证书撤销列表（CRL）配置文件的算法和标识符”，RFC 3279，2002年4月。
[RFC5480] Turner, S., Brown, D., Yiu, K., Housley, R., and T. Polk, "Elliptic Curve Cryptography Subject Public Key Information", RFC 5480, March 2009.
[RFC5480]Turner，S.，Brown，D.，Yiu，K.，Housley，R.，和T.Polk，“椭圆曲线加密主题公钥信息”，RFC 54802009年3月。
[SEC1] Certicom Research, "Elliptic Curve Cryptography", Standards for Efficient Cryptography (SEC) 1, September 2000.
[SEC1]Certicom Research，“椭圆曲线密码术”，高效密码标准（SEC）1，2000年9月。
[SEC2] Certicom Research, "Recommended Elliptic Curve Domain Parameters", Standards for Efficient Cryptography (SEC) 2, September 2000.
[SEC2]Certicom Research，“推荐的椭圆曲线域参数”，高效密码标准（SEC）2，2000年9月。
This section provides some test vectors for example Diffie-Hellman key exchanges using each of the curves defined in Table 1. The following notation is used in the subsequent sections:
本节提供了一些测试向量，例如使用表1中定义的每条曲线进行Diffie-Hellman密钥交换。以下符号用于后续章节：
d_A: the secret key of party A
d_A:甲方的秘密钥匙
x_qA: the x-coordinate of the public key of party A
x_qA：甲方公钥的x坐标
y_qA: the y-coordinate of the public key of party A
y_qA：甲方公钥的y坐标
d_B: the secret key of party B
d_B：乙方的秘密钥匙
x_qB: the x-coordinate of the public key of party B
x_qB：乙方公钥的x坐标
y_qB: the y-coordinate of the public key of party B
y_qB：乙方公钥的y坐标
x_Z: the x-coordinate of the shared secret that results from completion of the Diffie-Hellman computation, i.e., the hex representation of the pre-master secret
x_Z：由于Diffie-Hellman计算的完成而产生的共享秘密的x坐标，即前主秘密的十六进制表示
y_Z: the y-coordinate of the shared secret that results from completion of the Diffie-Hellman computation
y_Z：Diffie-Hellman计算完成后产生的共享秘密的y坐标
The field elements x_qA, y_qA, x_qB, y_qB, x_Z, and y_Z are represented as hexadecimal values using the FieldElement-to-OctetString conversion method specified in [SEC1].
字段元素x_-qA、y_-qA、x_-qB、y_-qB、x_-Z和y_-Z使用[SEC1]中指定的字段元素到八进制字符串的转换方法表示为十六进制值。
Curve brainpoolP256r1
曲线图P256R1
dA =
81DB1EE100150FF2EA338D708271BE38300CB54241D79950F77B063039804F1D
dA =
81DB1EE100150FF2EA338D708271BE38300CB54241D79950F77B063039804F1D
x_qA =
44106E913F92BC02A1705D9953A8414DB95E1AAA49E81D9E85F929A8E3100BE5
x_qA =
44106E913F92BC02A1705D9953A8414DB95E1AAA49E81D9E85F929A8E3100BE5
y_qA =
8AB4846F11CACCB73CE49CBDD120F5A900A69FD32C272223F789EF10EB089BDC
y_qA =
8AB4846F11CACCB73CE49CBDD120F5A900A69FD32C272223F789EF10EB089BDC
dB =
55E40BC41E37E3E2AD25C3C6654511FFA8474A91A0032087593852D3E7D76BD3
dB =
55E40BC41E37E3E2AD25C3C6654511FFA8474A91A0032087593852D3E7D76BD3
x_qB =
8D2D688C6CF93E1160AD04CC4429117DC2C41825E1E9FCA0ADDD34E6F1B39F7B
x_qB =
8D2D688C6CF93E1160AD04CC4429117DC2C41825E1E9FCA0ADDD34E6F1B39F7B
y_qB =
990C57520812BE512641E47034832106BC7D3E8DD0E4C7F1136D7006547CEC6A
y_qB =
990C57520812BE512641E47034832106BC7D3E8DD0E4C7F1136D7006547CEC6A
x_Z =
89AFC39D41D3B327814B80940B042590F96556EC91E6AE7939BCE31F3A18BF2B
x_Z =
89AFC39D41D3B327814B80940B042590F96556EC91E6AE7939BCE31F3A18BF2B
y_Z =
49C27868F4ECA2179BFD7D59B1E3BF34C1DBDE61AE12931648F43E59632504DE
y_Z =
49C27868F4ECA2179BFD7D59B1E3BF34C1DBDE61AE12931648F43E59632504DE
Curve brainpoolP384r1
曲线p384r1
dA = 1E20F5E048A5886F1F157C74E91BDE2B98C8B52D58E5003D57053FC4B0BD6
5D6F15EB5D1EE1610DF870795143627D042
dA = 1E20F5E048A5886F1F157C74E91BDE2B98C8B52D58E5003D57053FC4B0BD6
5D6F15EB5D1EE1610DF870795143627D042
x_qA = 68B665DD91C195800650CDD363C625F4E742E8134667B767B1B47679358
8F885AB698C852D4A6E77A252D6380FCAF068
x_qA = 68B665DD91C195800650CDD363C625F4E742E8134667B767B1B47679358
8F885AB698C852D4A6E77A252D6380FCAF068
y_qA = 55BC91A39C9EC01DEE36017B7D673A931236D2F1F5C83942D049E3FA206
07493E0D038FF2FD30C2AB67D15C85F7FAA59
y_qA = 55BC91A39C9EC01DEE36017B7D673A931236D2F1F5C83942D049E3FA206
07493E0D038FF2FD30C2AB67D15C85F7FAA59
dB = 032640BC6003C59260F7250C3DB58CE647F98E1260ACCE4ACDA3DD869F74E
01F8BA5E0324309DB6A9831497ABAC96670
dB = 032640BC6003C59260F7250C3DB58CE647F98E1260ACCE4ACDA3DD869F74E
01F8BA5E0324309DB6A9831497ABAC96670
x_qB = 4D44326F269A597A5B58BBA565DA5556ED7FD9A8A9EB76C25F46DB69D19
DC8CE6AD18E404B15738B2086DF37E71D1EB4
x_qB = 4D44326F269A597A5B58BBA565DA5556ED7FD9A8A9EB76C25F46DB69D19
DC8CE6AD18E404B15738B2086DF37E71D1EB4
y_qB = 62D692136DE56CBE93BF5FA3188EF58BC8A3A0EC6C1E151A21038A42E91
85329B5B275903D192F8D4E1F32FE9CC78C48
y_qB = 62D692136DE56CBE93BF5FA3188EF58BC8A3A0EC6C1E151A21038A42E91
85329B5B275903D192F8D4E1F32FE9CC78C48
x_Z = 0BD9D3A7EA0B3D519D09D8E48D0785FB744A6B355E6304BC51C229FBBCE2
39BBADF6403715C35D4FB2A5444F575D4F42
x_Z = 0BD9D3A7EA0B3D519D09D8E48D0785FB744A6B355E6304BC51C229FBBCE2
39BBADF6403715C35D4FB2A5444F575D4F42
y_Z = 0DF213417EBE4D8E40A5F76F66C56470C489A3478D146DECF6DF0D94BAE9
E598157290F8756066975F1DB34B2324B7BD
y_Z = 0DF213417EBE4D8E40A5F76F66C56470C489A3478D146DECF6DF0D94BAE9
E598157290F8756066975F1DB34B2324B7BD
Curve brainpoolP512r1
曲线p512r1
dA = 16302FF0DBBB5A8D733DAB7141C1B45ACBC8715939677F6A56850A38BD87B D59B09E80279609FF333EB9D4C061231FB26F92EEB04982A5F1D1764CAD5766542 2
dA=16302FF0DBBB5A8D733DAB7141C1B45ACBC8715939677F6A56850A38BD87B D59B09E80279609FF333EB9D4C061231FB26F92EEB04982A5F1D1764CAD5766542
x_qA = 0A420517E406AAC0ACDCE90FCD71487718D3B953EFD7FBEC5F7F27E28C6 149999397E91E029E06457DB2D3E640668B392C2A7E737A7F0BF04436D11640FD0 9FD
x_qA=0A420517E406AAC0ACDCE90FCD71487718D3B953EFD7FBEC5F7F27E28C6 14999397E91E029E06457DB2D3E640668B392A7E737A7F0BF04436D11640FD0 9FD
y_qA = 72E6882E8DB28AAD36237CD25D580DB23783961C8DC52DFA2EC138AD472 A0FCEF3887CF62B623B2A87DE5C588301EA3E5FC269B373B60724F5E82A6AD147F DE7
y_qA=72E6882E8DB28AAD36237CD25D580DB23783961C8DC52DFA2EC138AD472 A0FCEF3887CF62B623B2A87DE5C58801EA3E5FC269B373B60724F5E82A6AD147F DE7
dB = 230E18E1BCC88A362FA54E4EA3902009292F7F8033624FD471B5D8ACE49D1 2CFABBC19963DAB8E2F1EBA00BFFB29E4D72D13F2224562F405CB80503666B2542 9
dB=230E18E1BCC88A362FA54E4EA39020092F7F8033624FD471B5D8ACE49D1 2CFABBC19963DAB8E2F1EBA00BFFB29E4D72D13F2224562F405CB80503666B2542 9
x_qB = 9D45F66DE5D67E2E6DB6E93A59CE0BB48106097FF78A081DE781CDB31FC E8CCBAAEA8DD4320C4119F1E9CD437A2EAB3731FA9668AB268D871DEDA55A54731 99F
x_qB=9D45F66DE5D67E2E6DB6E93A59CE0BB48106097FF78A081DE781CDB31FC E8CCBAEA8DD4320C4119F1E9CD437A2EAB37331FA9668AB268D871DEDA55A54731 99F
y_qB = 2FDC313095BCDD5FB3A91636F07A959C8E86B5636A1E930E8396049CB48 1961D365CC11453A06C719835475B12CB52FC3C383BCE35E27EF194512B7187628 5FA
y_qB=2FDC313095BCDD5FB3A91636F07A959C8E86B56366A1E930E8396049CB48 1961D365CC1453A06C719835475B12CB52FC3C383BCE35E27EF194512B7187628 5FA
x_Z = A7927098655F1F9976FA50A9D566865DC530331846381C87256BAF322624 4B76D36403C024D7BBF0AA0803EAFF405D3D24F11A9B5C0BEF679FE1454B21C4CD 1F
x_Z=A7927098655F1F9976FA50A9D566865DC530331846381C87256BAF322624 4B76D36403C024DBF0AA0803EAFF405D3D24F11A9B5C0679FE1454B21C4CD 1F
y_Z = 7DB71C3DEF63212841C463E881BDCF055523BD368240E6C3143BD8DEF8B3 B3223B95E0F53082FF5E412F4222537A43DF1C6D25729DDB51620A832BE6A26680 A2
y_Z=7DB71C3DEF63212841C463E881BDCF05523BD368240E6C3143BD8DEF8B3223B95E0F53082FF5E412F4222537A43DF1C6D25729DDB51620A832BE6A26680 A2
Authors' Addresses
作者地址
Johannes Merkle secunet Security Networks Mergenthaler Allee 77 65760 Eschborn Germany
Johannes Merkle Secune安全网络Mergenthaler Allee 77 65760 Eschborn Germany
Phone: +49 201 5454 3091
EMail: johannes.merkle@secunet.com
Phone: +49 201 5454 3091
EMail: johannes.merkle@secunet.com
Manfred Lochter Bundesamt fuer Sicherheit in der Informationstechnik (BSI) Postfach 200363 53133 Bonn Germany
德国波恩信息技术学院（BSI）Postfach 200363 53133的Manfred Lochter Bundesamt fuer Sicherheit
Phone: +49 228 9582 5643
EMail: manfred.lochter@bsi.bund.de
Phone: +49 228 9582 5643
EMail: manfred.lochter@bsi.bund.de