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+Internet Engineering Task Force (IETF) D. Fu
+Request for Comments: 5903 J. Solinas
+Obsoletes: 4753 NSA
+Category: Informational June 2010
+ISSN: 2070-1721
+
+
+ Elliptic Curve Groups modulo a Prime (ECP Groups) for IKE and IKEv2
+
+Abstract
+
+ This document describes three 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. These groups are based on modular arithmetic rather
+ than binary arithmetic. These 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. This
+ document obsoletes RFC 4753.
+
+Status of This Memo
+
+ This document is not an Internet Standards Track specification; it is
+ published for informational purposes.
+
+ 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.
+
+ 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/rfc5903.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Fu & Solinas Informational [Page 1]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+Copyright Notice
+
+ Copyright (c) 2010 IETF Trust and the persons identified as the
+ document authors. All rights reserved.
+
+ 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.
+
+Table of Contents
+
+ 1. Introduction ....................................................3
+ 2. Requirements Terminology ........................................4
+ 3. Additional ECC Groups ...........................................4
+ 3.1. 256-Bit Random ECP Group ...................................4
+ 3.2. 384-Bit Random ECP Group ...................................5
+ 3.3. 521-Bit Random ECP Group ...................................6
+ 4. Security Considerations .........................................7
+ 5. Alignment with Other Standards ..................................7
+ 6. IANA Considerations .............................................7
+ 7. ECP Key Exchange Data Formats ...................................8
+ 8. Test Vectors ....................................................9
+ 8.1. 256-Bit Random ECP Group ...................................9
+ 8.2. 384-Bit Random ECP Group ..................................10
+ 8.3. 521-Bit Random ECP Group ..................................11
+ 9. Changes from RFC 4753 ..........................................13
+ 10. References ....................................................13
+ 10.1. Normative References .....................................13
+ 10.2. Informative References ...................................14
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Fu & Solinas Informational [Page 2]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+1. Introduction
+
+ 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].
+
+ 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. Nineteen additional groups subsequently have been
+ defined and assigned values by IANA. All of these additional groups
+ are optional.
+
+ 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.
+
+ - 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].)
+
+ - 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.)
+
+ - The groups proposed are capable of providing security consistent
+ with the Advanced Encryption Standard [AES].
+
+ 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.
+
+ These groups were originally proposed in [RFC4753]. This document
+ changes the format of the shared key produced by a Diffie-Hellman
+ exchange using these groups. The shared key format used in this
+ specification appeared earlier as an erratum to RFC 4753 [Err9], but
+ some implementors of RFC 4753 were unaware of the erratum and did not
+ implement the correction. Implementations of RFC 4753 that
+ incorporate the correction are interoperable with implementations of
+ this specification. However, there is a potential for
+ interoperability problems between implementations of this
+
+
+
+Fu & Solinas Informational [Page 3]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+ specification and implementations of RFC 4753 that did not implement
+ the correction from the erratum. These problems could be difficult
+ to detect and analyze since both use the same code point but the
+ secret value (which is probably not available to the trouble desk) is
+ computed differently. Where peers are not interoperable, the
+ initiator will never receive a response and eventually times out.
+
+ Section 9 provides more details of the changes from [RFC4753]. This
+ document obsoletes RFC 4753 and addresses the erratum.
+
+2. Requirements Terminology
+
+ The key words "MUST" and "SHOULD" that appear in this document are to
+ be interpreted as described in [RFC2119].
+
+3. Additional ECC Groups
+
+ The notation adopted in RFC 2409 [IKE] is used below to describe the
+ groups proposed.
+
+3.1. 256-Bit Random ECP Group
+
+ 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:
+
+ p = 2^(256)-2^(224)+2^(192)+2^(96)-1
+
+ The equation for the elliptic curve is:
+
+ y^2 = x^3 - 3 x + b
+
+Field Size:
+ 256
+
+Group Prime/Irreducible Polynomial:
+ FFFFFFFF 00000001 00000000 00000000 00000000 FFFFFFFF FFFFFFFF FFFFFFFF
+
+Group Curve b:
+ 5AC635D8 AA3A93E7 B3EBBD55 769886BC 651D06B0 CC53B0F6 3BCE3C3E 27D2604B
+
+Group Order:
+ FFFFFFFF 00000000 FFFFFFFF FFFFFFFF BCE6FAAD A7179E84 F3B9CAC2 FC632551
+
+ The group was chosen verifiably at random using SHA-1 as specified
+ in [IEEE-1363] from the seed:
+
+ C49D3608 86E70493 6A6678E1 139D26B7 819F7E90
+
+
+
+Fu & Solinas Informational [Page 4]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+ The generator for this group is given by g=(gx,gy) where:
+
+gx:
+ 6B17D1F2 E12C4247 F8BCE6E5 63A440F2 77037D81 2DEB33A0 F4A13945 D898C296
+
+gy:
+ 4FE342E2 FE1A7F9B 8EE7EB4A 7C0F9E16 2BCE3357 6B315ECE CBB64068 37BF51F5
+
+3.2. 384-Bit Random ECP Group
+
+ 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:
+
+ p = 2^(384)-2^(128)-2^(96)+2^(32)-1
+
+ The equation for the elliptic curve is:
+
+ y^2 = x^3 - 3 x + b
+
+Field Size:
+ 384
+
+Group Prime/Irreducible Polynomial:
+ FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE
+ FFFFFFFF 00000000 00000000 FFFFFFFF
+
+Group Curve 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
+
+ The group was chosen verifiably at random using SHA-1 as specified
+ in [IEEE-1363] from the seed:
+
+ A335926A A319A27A 1D00896A 6773A482 7ACDAC73
+ The generator for this group is given by g=(gx,gy) where:
+
+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
+
+
+
+Fu & Solinas Informational [Page 5]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+3.3. 521-Bit Random ECP Group
+
+ 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:
+
+ p = 2^(521)-1
+
+ The equation for the elliptic curve is:
+
+ y^2 = x^3 - 3 x + b
+
+Field Size:
+ 521
+
+Group Prime/Irreducible Polynomial:
+ 01FFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF
+ FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF
+ FFFF
+
+Group Curve 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
+
+ The group was chosen verifiably at random using SHA-1 as specified
+ in [IEEE-1363] from the seed:
+
+ D09E8800 291CB853 96CC6717 393284AA A0DA64BA
+
+ The generator for this group is given by g=(gx,gy) where:
+
+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
+
+
+
+
+
+Fu & Solinas Informational [Page 6]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+4. Security Considerations
+
+ Since this document proposes groups for use within IKE and IKEv2,
+ many of the security considerations contained within [IKE] and
+ [IKEv2] apply here as well.
+
+ 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].
+
+5. Alignment with Other Standards
+
+ The following table summarizes the appearance of these three elliptic
+ curve groups in other standards.
+
+ 256-Bit 384-Bit 521-Bit
+ Random Random Random
+ Standard ECP Group ECP Group ECP Group
+ ----------- ------------ ------------ ------------
+
+ NIST [DSS] P-256 P-384 P-521
+
+ ISO/IEC [ISO-15946-1] P-256
+
+ 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 [X9.63] Sect. J.5.4, Sect. J.5.5 Sect. J.5.6
+ Example 2
+
+ SECG [SEC2] secp256r1 secp384r1 secp521r1
+
+ See also [NIST], [ISO-14888-3], [ISO-15946-2], [ISO-15946-3], and
+ [ISO-15946-4].
+
+6. IANA Considerations
+
+ 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.
+
+ In [IANA-IKE], the groups appear as entries in the list of Diffie-
+ Hellman groups given by Group Description (attribute class 4).
+
+
+
+
+
+Fu & Solinas Informational [Page 7]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+ The descriptions are "256-bit random ECP group", "384-bit random ECP
+ 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]).
+
+ In [IANA-IKEv2], the groups appear as entries in the list of IKEv2
+ transform type values for Transform Type 4 (Diffie-Hellman groups).
+
+ These entries in both [IANA-IKE] and [IANA-IKEv2] have been updated.
+ The update consisted of changing the reference from [RFC4753] to this
+ document.
+
+7. ECP Key Exchange Data Formats
+
+ 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.
+
+ Diffie-Hellman group component bit length
+ ------------------------ --------------------
+
+ 256-bit Random ECP Group 256
+ 384-bit Random ECP Group 384
+ 521-bit Random ECP Group 528
+
+ This length is enforced, if necessary, by prepending the value with
+ zeros.
+
+ The Diffie-Hellman public value is obtained by concatenating the x
+ and y values.
+
+ The Diffie-Hellman shared secret value consists of the x value of the
+ Diffie-Hellman common value.
+
+ These formats should be regarded as specific to ECP curves and may
+ not be applicable to EC2N (elliptic curve group over GF[2^N]) curves.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Fu & Solinas Informational [Page 8]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+8. Test Vectors
+
+ The following are examples of the IKEv2 key exchange payload for each
+ of the three groups specified in this document.
+
+ 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].
+
+8.1. 256-Bit Random ECP Group
+
+ IANA assigned the ID value 19 to this Diffie-Hellman group.
+
+ We suppose that the initiator's Diffie-Hellman private key is:
+
+i:
+ C88F01F5 10D9AC3F 70A292DA A2316DE5 44E9AAB8 AFE84049 C62A9C57 862D1433
+
+ Then the public key is given by g^i=(gix,giy) where:
+
+gix:
+ DAD0B653 94221CF9 B051E1FE CA5787D0 98DFE637 FC90B9EF 945D0C37 72581180
+
+giy:
+ 5271A046 1CDB8252 D61F1C45 6FA3E59A B1F45B33 ACCF5F58 389E0577 B8990BB3
+
+ The KEi payload is as follows.
+
+ 00000048 00130000 DAD0B653 94221CF9 B051E1FE CA5787D0 98DFE637 FC90B9EF
+ 945D0C37 72581180 5271A046 1CDB8252 D61F1C45 6FA3E59A B1F45B33 ACCF5F58
+ 389E0577 B8990BB3
+
+ We suppose that the response Diffie-Hellman private key is:
+
+r:
+ C6EF9C5D 78AE012A 011164AC B397CE20 88685D8F 06BF9BE0 B283AB46 476BEE53
+
+ Then the public key is given by g^r=(grx,gry) where:
+
+grx:
+ D12DFB52 89C8D4F8 1208B702 70398C34 2296970A 0BCCB74C 736FC755 4494BF63
+
+gry:
+ 56FBF3CA 366CC23E 8157854C 13C58D6A AC23F046 ADA30F83 53E74F33 039872AB
+
+ The KEr payload is as follows.
+
+
+
+
+Fu & Solinas Informational [Page 9]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+ 00000048 00130000 D12DFB52 89C8D4F8 1208B702 70398C34 2296970A 0BCCB74C
+ 736FC755 4494BF63 56FBF3CA 366CC23E 8157854C 13C58D6A AC23F046 ADA30F83
+ 53E74F33 039872AB
+
+ The Diffie-Hellman common value (girx,giry) is:
+
+girx:
+ D6840F6B 42F6EDAF D13116E0 E1256520 2FEF8E9E CE7DCE03 812464D0 4B9442DE
+
+giry:
+ 522BDE0A F0D8585B 8DEF9C18 3B5AE38F 50235206 A8674ECB 5D98EDB2 0EB153A2
+
+ The Diffie-Hellman shared secret value is girx.
+
+8.2. 384-Bit Random ECP Group
+
+ IANA assigned the ID value 20 to this Diffie-Hellman group.
+
+ We suppose that the initiator's Diffie-Hellman private key is:
+
+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:
+
+gix:
+ 667842D7 D180AC2C DE6F74F3 7551F557 55C7645C 20EF73E3 1634FE72 B4C55EE6
+ DE3AC808 ACB4BDB4 C88732AE E95F41AA
+
+giy:
+ 9482ED1F C0EEB9CA FC498462 5CCFC23F 65032149 E0E144AD A0241815 35A0F38E
+ EB9FCFF3 C2C947DA E69B4C63 4573A81C
+
+ The KEi payload is as follows.
+
+ 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
+
+ We suppose that the response Diffie-Hellman private key is:
+
+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:
+
+
+
+Fu & Solinas Informational [Page 10]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+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
+
+ The KEr payload is as follows.
+
+ 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
+
+ The Diffie-Hellman common value (girx,giry) is:
+
+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
+
+ The Diffie-Hellman shared secret value is girx.
+
+8.3. 521-Bit Random ECP Group
+
+ IANA assigned the ID value 21 to this Diffie-Hellman group.
+
+ We suppose that the initiator's Diffie-Hellman private key is:
+
+i:
+ 0037ADE9 319A89F4 DABDB3EF 411AACCC 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:
+
+gix:
+ 0015417E 84DBF28C 0AD3C278 713349DC 7DF153C8 97A1891B D98BAB43 57C9ECBE
+ E1E3BF42 E00B8E38 0AEAE57C 2D107564 94188594 2AF5A7F4 601723C4 195D176C
+ ED3E
+
+
+
+
+
+
+
+Fu & Solinas Informational [Page 11]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+giy:
+ 017CAE20 B6641D2E EB695786 D8C94614 6239D099 E18E1D5A 514C739D 7CB4A10A
+ D8A78801 5AC405D7 799DC75E 7B7D5B6C F2261A6A 7F150743 8BF01BEB 6CA3926F
+ 9582
+
+ The KEi payload is as follows.
+
+ 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
+
+ We suppose that the response Diffie-Hellman private key is:
+
+r:
+ 0145BA99 A847AF43 793FDD0E 872E7CDF A16BE30F DC780F97 BCCC3F07 8380201E
+ 9C677D60 0B343757 A3BDBF2A 3163E4C2 F869CCA7 458AA4A4 EFFC311F 5CB15168
+ 5EB9
+
+ Then the public key is given by g^r=(grx,gry) where:
+
+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
+
+ The KEr payload is as follows.
+
+ 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
+
+ The Diffie-Hellman common value (girx,giry) is:
+
+girx:
+ 01144C7D 79AE6956 BC8EDB8E 7C787C45 21CB086F A64407F9 7894E5E6 B2D79B04
+ D1427E73 CA4BAA24 0A347868 59810C06 B3C715A3 A8CC3151 F2BEE417 996D19F3
+ DDEA
+
+
+
+
+
+Fu & Solinas Informational [Page 12]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+giry:
+ 01B901E6 B17DB294 7AC017D8 53EF1C16 74E5CFE5 9CDA18D0 78E05D1B 5242ADAA
+ 9FFC3C63 EA05EDB1 E13CE5B3 A8E50C3E B622E8DA 1B38E0BD D1F88569 D6C99BAF
+ FA43
+
+ The Diffie-Hellman shared secret value is girx.
+
+9. Changes from RFC 4753
+
+ Section 7 (ECP Key Exchange Data Formats) of [RFC4753] states that
+
+ The Diffie-Hellman public value is obtained by concatenating the x
+ and y values.
+
+ The format of the Diffie-Hellman shared secret value is the same
+ as that of the Diffie-Hellman public value.
+
+ This document replaces the second of these two paragraphs with the
+ following:
+
+ The Diffie-Hellman shared secret value consists of the x value of
+ the Diffie-Hellman common value.
+
+ This change aligns the ECP key exchange format with that used in
+ other standards.
+
+ This change appeared earlier as an erratum to RFC 4753 [Err9]. This
+ document obsoletes RFC 4753 and addresses the erratum.
+
+ Section 8 (Test Vectors) of [RFC4753] provides three examples of
+ Diffie-Hellman key agreement using the ECP groups. This document
+ changes the last paragraph of each subsection of Section 8 to reflect
+ the new format.
+
+10. References
+
+10.1. Normative References
+
+ [IANA-IKE] Internet Assigned Numbers Authority, "Internet Key
+ Exchange (IKE) Attributes", <http://www.iana.org>.
+
+ [IANA-IKEv2] Internet Assigned Numbers Authority, "Internet Key
+ Exchange Version 2 (IKEv2) Parameters",
+ <http://www.iana.org>.
+
+ [IKE] Harkins, D. and D. Carrel, "The Internet Key Exchange
+ (IKE)", RFC 2409, November 1998.
+
+
+
+
+Fu & Solinas Informational [Page 13]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+ [IKEv2] Kaufman, C., Ed., "Internet Key Exchange (IKEv2)
+ Protocol", RFC 4306, December 2005.
+
+ [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
+ Requirement Levels", BCP 14, RFC 2119, March 1997.
+
+ [RFC4753] Fu, D. and J. Solinas, "ECP Groups For IKE and IKEv2",
+ RFC 4753, January 2007.
+
+10.2. Informative References
+
+ [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>.
+
+ [Err9] RFC Errata, Errata ID 9, RFC 4753,
+ <http://www.rfc-editor.org>.
+
+ [GMN] J. Solinas, Generalized Mersenne Numbers,
+ Combinatorics and Optimization Research Report 99-39,
+ 1999, <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>.
+
+ [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-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.
+
+
+
+
+
+
+
+
+Fu & Solinas Informational [Page 14]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+ [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-15946-3] 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-15946-4] 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-18031] International Organization for Standardization and
+ International Electrotechnical Commission, ISO/IEC
+ 18031:2005, Information Technology: Security
+ Techniques: Random Bit Generation.
+
+ [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
+ 800-56A, March 2006,
+ <http://csrc.nist.gov/CryptoToolkit/KeyMgmt.html>.
+
+ [SEC2] Standards for Efficient Cryptography Group. SEC 2 -
+ Recommended Elliptic Curve Domain Parameters, 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.
+
+ [X9.62-2005] American National Standards Institute, X9.62:2005:
+ Public Key Cryptography for the Financial Services
+ Industry: The Elliptic Curve Digital Signature
+ Algorithm (ECDSA).
+
+
+
+
+
+
+
+Fu & Solinas Informational [Page 15]
+
+RFC 5903 ECP Groups for IKE and IKEv2 June 2010
+
+
+ [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.
+
+Authors' Addresses
+
+ David E. Fu
+ National Information Assurance Research Laboratory
+ National Security Agency
+
+ EMail: defu@orion.ncsc.mil
+
+
+ Jerome A. Solinas
+ National Information Assurance Research Laboratory
+ National Security Agency
+
+ EMail: jasolin@orion.ncsc.mil
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Fu & Solinas Informational [Page 16]
+