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Versions: 00 01 02 03 04 RFC 6932

Internet Engineering Task Force                          D. Harkins, Ed.
Internet-Draft                                            Aruba Networks
Intended status: Informational                          October 22, 2012
Expires: April 25, 2013


    Brainpool Elliptic Curves for the IKE Group Description Registry
                 draft-harkins-brainpool-ike-groups-01

Abstract

   This memo allocates code points for eight new elliptic curve domain
   parameter sets over finite prime fields into a registry established
   by The Internet Key Exchange (IKE).

Status of this Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
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   This Internet-Draft will expire on April 25, 2013.

Copyright Notice

   Copyright (c) 2012 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
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   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.





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Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
     1.1.  Requirements Language  . . . . . . . . . . . . . . . . . .  3
   2.  Brainpool Elliptic Curves  . . . . . . . . . . . . . . . . . .  3
     2.1.  Domain Parameters for 224-bit Curves . . . . . . . . . . .  4
       2.1.1.  Curve-ID: brainpoolP224r1  . . . . . . . . . . . . . .  4
       2.1.2.  Twisted Curve-ID: brainpoolP224t1  . . . . . . . . . .  5
     2.2.  Domain Parameters for 256-bit Curves . . . . . . . . . . .  5
       2.2.1.  Curve-ID: brainpoolP256r1  . . . . . . . . . . . . . .  5
       2.2.2.  Twisted Curve-ID: brainpoolP256t1  . . . . . . . . . .  6
     2.3.  Domain Parameters for 384-bit Curves . . . . . . . . . . .  6
       2.3.1.  Curve-ID: brainpoolP384r1  . . . . . . . . . . . . . .  6
       2.3.2.  Twisted Curve-ID: brainpoolP384t1  . . . . . . . . . .  7
     2.4.  Domain Parameters for 512-bit Curves . . . . . . . . . . .  7
       2.4.1.  Curve-ID: brainpoolP512r1  . . . . . . . . . . . . . .  8
       2.4.2.  Twisted Curve-ID: brainpoolP512t1  . . . . . . . . . .  9
   3.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . .  9
   4.  Security Considerations  . . . . . . . . . . . . . . . . . . . 10
   5.  References . . . . . . . . . . . . . . . . . . . . . . . . . . 10
     5.1.  Normative References . . . . . . . . . . . . . . . . . . . 10
     5.2.  Informative References . . . . . . . . . . . . . . . . . . 10
   Appendix A.  Appendix A: Test Data . . . . . . . . . . . . . . . . 11
     A.1.  brainpoolP224r1  . . . . . . . . . . . . . . . . . . . . . 12
     A.2.  brainpoolP224t1  . . . . . . . . . . . . . . . . . . . . . 13
     A.3.  brainpoolP256r1  . . . . . . . . . . . . . . . . . . . . . 14
     A.4.  brainpoolP256t1  . . . . . . . . . . . . . . . . . . . . . 15
     A.5.  brainpoolP384r1  . . . . . . . . . . . . . . . . . . . . . 16
     A.6.  brainpoolP384t1  . . . . . . . . . . . . . . . . . . . . . 17
     A.7.  brainpoolP512r1  . . . . . . . . . . . . . . . . . . . . . 18
     A.8.  brainpoolP512t1  . . . . . . . . . . . . . . . . . . . . . 19
   Author's Address . . . . . . . . . . . . . . . . . . . . . . . . . 19



















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1.  Introduction

   [RFC5639] defines new elliptic curve domain parmaeters for curves
   over a number of different prime fields, each with a "twisted"
   varient.  These curves have a number of interesting security
   properties (as described in [EBP]) that make them desirable to use.

   IANA maintains a registry for [RFC2409] to map complete domain
   parameter sets into easily-referenced numbers.  While [RFC2409] is
   deprecated, other protocols, for example [IEEE802.11] and [RFC5931],
   refer to this registry for its convenience.  Therefore, this memo
   instructs IANA to allocate new code points for the Brainpool curves
   defined in [RFC5639] to the registry established by [RFC2409].

1.1.  Requirements Language

   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].


2.  Brainpool Elliptic Curves

   [RFC5639] defines several elliptic curves over finite prime fields
   (ECP, in the parlance of [RFC2409]).  The domain parameter sets for
   each of the elliptic curves defined in [RFC5639] and are copied here
   for convenient reference.

   The equation for all elliptic curves defined here is:

      y^2 = x^3 + ax + b (mod p)

   Domain parameter sets consist of:

   o  p: the prime

   o  a, b: parameters to the equation of the curve

   o  x, y: the coordinates of the generator for the group, G

   o  q: the order of the group formed by the generator G

   o  h: the co-factor

   o  z: the "twist" (for twisted curves only)

   The prime used with the twisted curve is the same as its untwisted
   sibling-- that is, brainpoolP256t1 uses "p" from brainpoolP256r1.



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   Parameter z is used for the quadratic twist to generate the
   parameters for the twisted varients.  See [EBP] for more information.

   [RFC5639] defines elliptic curves over seven (7) prime fields with a
   "twisted" and non-"twisted" variety for each, for a total of fourteen
   (14) distinct curves.  Six (6) of those curves, though, are not
   particularly useful: the 160-bit curves provide only 80 bits of
   strength and that is too small to be of use in current cryptographic
   applications, and there is no standard hash function to use with the
   196-bit and 320-bit curves-- it would make more sense to use the 224-
   bit and 384-bit curves, respectively, instead.  For those reasons,
   the "twisted" and non-"twisted" curves over the 160-bit, 192-bit and
   320-bit curves are not being added to the registry created by
   [RFC2409].

2.1.  Domain Parameters for 224-bit Curves

2.1.1.  Curve-ID: brainpoolP224r1

   p = D7C134AA264366862A18302575D1D787B09F075797DA89F57EC8C0FF

   A = 68A5E62CA9CE6C1C299803A6C1530B514E182AD8B0042A59CAD29F43

   B = 2580F63CCFE44138870713B1A92369E33E2135D266DBB372386C400B

   x = 0D9029AD2C7E5CF4340823B2A87DC68C9E4CE3174C1E6EFDEE12C07D

   y = 58AA56F772C0726F24C6B89E4ECDAC24354B9E99CAA3F6D3761402CD

   q = D7C134AA264366862A18302575D0FB98D116BC4B6DDEBCA3A5A7939F

   h = 1



















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2.1.2.  Twisted Curve-ID: brainpoolP224t1

   z = 2DF271E14427A346910CF7A2E6CFA7B3F484E5C2CCE1C8B730E28B3F

   A = D7C134AA264366862A18302575D1D787B09F075797DA89F57EC8C0FC

   B = 4B337D934104CD7BEF271BF60CED1ED20DA14C08B3BB64F18A60888D

   x = 6AB1E344CE25FF3896424E7FFE14762ECB49F8928AC0C76029B4D580

   y = 0374E9F5143E568CD23F3F4D7C0D4B1E41C8CC0D1C6ABD5F1A46DB4C

   q = D7C134AA264366862A18302575D0FB98D116BC4B6DDEBCA3A5A7939F

   h = 1

2.2.  Domain Parameters for 256-bit Curves

2.2.1.  Curve-ID: brainpoolP256r1

   p = A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377

   A = 7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9

   B = 26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6

   x = 8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262

   y = 547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997

   q = A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7

   h = 1


















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2.2.2.  Twisted Curve-ID: brainpoolP256t1

   z = 3E2D4BD9597B58639AE7AA669CAB9837CF5CF20A2C852D10F655668DFC150EF0

   A = A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5374

   B = 662C61C430D84EA4FE66A7733D0B76B7BF93EBC4AF2F49256AE58101FEE92B04

   x = A3E8EB3CC1CFE7B7732213B23A656149AFA142C47AAFBC2B79A191562E1305F4

   y = 2D996C823439C56D7F7B22E14644417E69BCB6DE39D027001DABE8F35B25C9BE

   q = A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7

   h = 1

2.3.  Domain Parameters for 384-bit Curves

2.3.1.  Curve-ID: brainpoolP384r1

   p = 8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB711
       23ACD3A729901D1A71874700133107EC53

   A = 7BC382C63D8C150C3C72080ACE05AFA0C2BEA28E4FB22787139165EFBA91F9
       0F8AA5814A503AD4EB04A8C7DD22CE2826

   B = 04A8C7DD22CE28268B39B55416F0447C2FB77DE107DCD2A62E880EA53EEB62
       D57CB4390295DBC9943AB78696FA504C11

   x = 1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10
       E8E826E03436D646AAEF87B2E247D4AF1E

   y = 8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129
       280E4646217791811142820341263C5315

   q = 8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425
       A7CF3AB6AF6B7FC3103B883202E9046565

   h = 1












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2.3.2.  Twisted Curve-ID: brainpoolP384t1

   z = 41DFE8DD399331F7166A66076734A89CD0D2BCDB7D068E44E1F378F41ECBAE
       97D2D63DBC87BCCDDCCC5DA39E8589291C

   A = 8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB711
       23ACD3A729901D1A71874700133107EC50

   B = 7F519EADA7BDA81BD826DBA647910F8C4B9346ED8CCDC64E4B1ABD11756DCE
       1D2074AA263B88805CED70355A33B471EE

   x = 18DE98B02DB9A306F2AFCD7235F72A819B80AB12EBD653172476FECD462AAB
       FFC4FF191B946A5F54D8D0AA2F418808CC

   y = 25AB056962D30651A114AFD2755AD336747F93475B7A1FCA3B88F2B6A208CC
       FE469408584DC2B2912675BF5B9E582928

   q = 8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425
       A7CF3AB6AF6B7FC3103B883202E9046565

   h = 1

2.4.  Domain Parameters for 512-bit Curves




























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2.4.1.  Curve-ID: brainpoolP512r1

   p = AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308
       717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A
       48F3

   A = 7830A3318B603B89E2327145AC234CC594CBDD8D3DF91610A83441CAEA9863
       BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC
       94CA

   B = 3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117
       A72BF2C7B9E7C1AC4D77FC94CADC083E67984050B75EBAE5DD2809BD638016
       F723

   x = 81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D009
       8EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9
       F822

   y = 7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F81
       11B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD8
       0892

   q = AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308
       70553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA9
       0069

   h = 1
























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2.4.2.  Twisted Curve-ID: brainpoolP512t1

   z = 12EE58E6764838B69782136F0F2D3BA06E27695716054092E60A80BEDB212B
       64E585D90BCE13761F85C3F1D2A64E3BE8FEA2220F01EBA5EEB0F35DBD29D9
       22AB

   A = AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308
       717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A
       48F0

   B = 7CBBBCF9441CFAB76E1890E46884EAE321F70C0BCB4981527897504BEC3E36
       A62BCDFA2304976540F6450085F2DAE145C22553B465763689180EA2571867
       423E

   x = 640ECE5C12788717B9C1BA06CBC2A6FEBA85842458C56DDE9DB1758D39C031
       3D82BA51735CDB3EA499AA77A7D6943A64F7A3F25FE26F06B51BAA2696FA90
       35DA

   y = 5B534BD595F5AF0FA2C892376C84ACE1BB4E3019B71634C01131159CAE03CE
       E9D9932184BEEF216BD71DF2DADF86A627306ECFF96DBB8BACE198B61E00F8
       B332

   q = AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308
       70553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA9
       0069

   h = 1


3.  IANA Considerations

   IANA is instructed to update the [IANA-IKE] registry entitled "Group
   description" by adding the contents of Table 1, replacing TBD1-TBD8
   with the next contiguous eight (8) unassigned values, replacing the
   phrase "this memo" with the reference to the assigned RFC number this
   memo receives.















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   +-------+-------------------------------+-----------+---------------+
   | Value |       Group Description       | Reference |      Note     |
   +-------+-------------------------------+-----------+---------------+
   |  TBD1 |  224-bit Brainpool ECP group  | this memo | Section 2.1.1 |
   |  TBD2 | 224-bit Brainpool twisted ECP | this memo | Section 2.1.2 |
   |       |             group             |           |               |
   |  TBD3 |  256-bit Brainpool ECP group  | this memo | Section 2.2.1 |
   |  TBD4 | 256-bit Brainpool twisted ECP | this memo | Section 2.2.2 |
   |       |             group             |           |               |
   |  TBD5 |  384-bit Brainpool ECP group  | this memo | Section 2.3.1 |
   |  TBD6 | 384-bit Brainpool twisted ECP | this memo | Section 2.3.2 |
   |       |             group             |           |               |
   |  TBD7 |  512-bit Brainpool ECP group  | this memo | Section 2.4.1 |
   |  TBD8 | 512-bit Brainpool twisted ECP | this memo | Section 2.4.2 |
   |       |             group             |           |               |
   +-------+-------------------------------+-----------+---------------+

                    Table 1: Group Description Updates


4.  Security Considerations

   [EBP] describes the security properties of the curves referenced
   here.  The curves support security levels of 112 (Section 2.1), 128
   (Section 2.2), 192 (Section 2.3), and 256 (Section 2.4).


5.  References

5.1.  Normative References

   [IANA-IKE]
              IANA, "Internet Key Exchange (IKE) Attributes", Registry
              Name: Group Description (Value 4), 2012, <http://
              www.iana.org/assignments/ipsec-registry/
              ipsec-registry.xml>.

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

   [RFC5639]  Lochter, M. and J. Merkle, "Elliptic Curve Cryptography
              (ECC) Brainpool Standard Curves and Curve Generation",
              RFC 5639, March 2010.

5.2.  Informative References

   [EBP]      The Brainpool Workgroup, "ECC Brainpool Standard Curves
              and Curge Generation", Brainpool: http://



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              www.ecc-brainpool.org/download/Domain-parameters.pdf,
              October 2005.

   [IEEE802.11]
              IEEE Computer Society, "Telecommunications and information
              exchange between systems Local and metropolitan area
              networks--",  Part 11: Wireless LAN Medium Access Control
              (MAC) and Physical  Layer (PHY) Specifications IEEE Std
              802.11-2012.

   [RFC2409]  Harkins, D. and D. Carrel, "The Internet Key Exchange
              (IKE)", RFC 2409, November 1998.

   [RFC5931]  Harkins, D. and G. Zorn, "Extensible Authentication
              Protocol (EAP) Authentication Using Only a Password",
              RFC 5931, August 2010.


Appendix A.  Appendix A: Test Data

   This section provides some test vectors for example Diffie-Hellman
   key exchanges using each of the curves defined in Section 2.  In all
   of the following sections the following notation is used:

   o  dA: the secret key of party A

   o  x_qA: the x-coordinate of the public key of party A

   o  y_qA: the y-coordinate of the public key of party A

   o  dB: the secret key of party B

   o  x_qB: the x-coordinate of the public key of party B

   o  y_qB: the y-coordinate of the public key of party B

   o  x_Z: the x-coordinate of the shared secret that results from
      completion of the Diffie-Hellman computation

   o  y_Z: the y-coordinate of the shared secret that results from
      completion of the Diffie-Hellman computation










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A.1.  brainpoolP224r1

   dA =
   7C4B7A2C 8A4BAD1F BB7D79CC 0955DB7C 6A4660CA 64CC4778
   159B495E

   x_qA =
   B104A67A 6F6E85E1 4EC1825E 1539E8EC DBBF5849 22367DD8
   8C6BDCF2
   y_qA =
   46D782E7 FDB5F60C D8404301 AC5949C5 8EDB26BC 68BA0769
   5B750A94

   dB =
   63976D4A AE6CD0F6 DD18DEFE F55D9656 9D0507C0 3E74D648
   6FFA28FB

   x_qB =
   2A97089A 9296147B 71B21A4B 574E1278 245B536F 14D8C2B9
   D07A874E
   y_qB =
   9B900D7C 77A709A7 97276B8C A1BA61BB 95B546FC 29F862E4
   4D59D25B

   x_Z =
   312DFD98 783F9FB7 7B970494 5A73BEB6 DCCBE3B6 5D0F967D
   CAB574EB
   y_Z =
   6F800811 D64114B1 C48C621A B3357CF9 3F496E42 38696A2A
   012B3C98





















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A.2.  brainpoolP224t1

   dA =
   4013CDB4 211913EC A752F322 550FE689 BB690257 4B0E1B2E
   5FA061A0

   x_qA =
   439DDE17 6DF6A02D F7DB11DA 06C113AD 6B8B451C 795ED973
   48BF92B6
   y_qA =
   7BF4B135 3191D441 B8D16837 B6FEFA35 FE9CC5E1 A0E1FFAA
   E1366EDD

   dB =
   A819C6F5 5D515BA2 3629BC41 E2DC413D E3BB7E8F 0450E2B2
   DB830DCA

   x_qB =
   6E500417 2CA87C9C B8EE2496 F25584E5 5D027CE3 44F125BA
   A499CE7B
   y_qB =
   A84A4612 2EE9C474 491F3981 4428B6F5 6A1A6C17 CF1290A6
   30BD5F76

   x_Z =
   3B6CE732 1926C051 0C0CB52E 45919F9F 793EBD4E C0D7A480
   097240B2
   y_Z =
   9B54102D 91ACE9BB AC21AC3E A3C13175 87817AD3 3675F412
   952269F2





















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A.3.  brainpoolP256r1

   dA =
   041EB8B1 E2BC681B CE8E3996 3B2E9FC4 15B05283 313DD1A8
   BCC055F1 1AE49699

   x_qA =
   78028496 B5ECAAB3 C8B6C12E 45DB1E02 C9E4D26B 4113BC4F
   015F60C5 CCC0D206
   y_qA =
   A2AE1762 A3831C1D 20F03F8D 1E3C0C39 AFE6F09B 4D44BBE8
   0CD10098 7B05F92B

   dB =
   06F5240E ACDB9837 BC96D482 74C8AA83 4B6C87BA 9CC3EEDD
   81F99A16 B8D804D3

   x_qB =
   8E07E219 BA588916 C5B06AA3 0A2F464C 2F2ACFC1 610A3BE2
   FB240B63 5341F0DB
   y_qB =
   148EA1D7 D1E7E54B 9555B6C9 AC90629C 18B63BEE 5D7AA694
   9EBBF47B 24FDE40D

   x_Z =
   05E94091 5549E9F6 A4A75693 716E3746 6ABA79B4 BF291987
   7A16DD2C C2E23708
   y_Z =
   6BC23B67 02BC5A01 9438CEEA 107DAAD8 B94232FF BBC350F3
   B137628F E6FD134C





















Harkins                  Expires April 25, 2013                [Page 14]

Internet-Draft     Brainpool EC for IKE Group Registry      October 2012


A.4.  brainpoolP256t1

   dA =
   743824FA 3C874DDD E4B3899A 18A97FC5 AB5C155D B97552A0
   CD8679DC 934BA25E

   x_qA =
   2495D40D 0FED9A51 3C6744D5 8C992340 097B2498 B1B7FEA3
   BC97381F A96480E2
   y_qA =
   36E0DD1A BC0AB311 2886176C 0DF22353 56D61D07 82ACA9E9
   321C87EA 3279151E

   dB =
   5AD80D63 5C3C3D35 707D871B 63DB5CBD 17DBDE14 517ED8B6
   A3D8FAA6 E1AEE487

   x_qB =
   2BA62E40 C2834E20 7EF5E6F9 80E9E94D 11E5A24F 74A694AC
   1019D742 997CBD37
   y_qB =
   24452ED7 8BA85960 370F150A 542C0668 1CC96AD4 F318E89D
   C14B08C6 3E0CF4D4

   x_Z =
   5043E1CD 1ED80FE0 15C92DDB B4C6A677 CFF79879 8E3DBC23
   0EFD26E7 35630955
   y_Z =
   1ACE763C F6BD85EE FFE8E074 46645EF0 0507DE93 2018D999
   A77A6D5C 492BA645





















Harkins                  Expires April 25, 2013                [Page 15]

Internet-Draft     Brainpool EC for IKE Group Registry      October 2012


A.5.  brainpoolP384r1

   dA =
   014EC075 5B78594B A47FB0A5 6F617304 5B4331E7 4BA1A6F4
   7322E70D 79D828D9 7E095884 CA72B73F DABD5910 DF0FA76A

   x_qA =
   45CB26E4 384DAF6F B7768853 07B9A38B 7AD1B5C6 92E0C32F
   01253327 78F3B8D3 F50CA358 099B30DE B5EE69A9 5C058B4E
   y_qA =
   8173A1C5 4AFFA7E7 81D0E1E1 D12C0DC2 B74F4DF5 8E4A4E3A
   F7026C5D 32DC530A 2CD89C85 9BB4B4B7 68497F49 AB8CC859

   dB =
   6B461CB7 9BD0EA51 9A87D682 8815D8CE 7CD9B3CA A0B5A826
   2CBCD550 A015C900 95B976F3 52995750 6E1224A8 61711D54

   x_qB =
   01BF92A9 2EE4BE8D ED1A9111 25C209B0 3F99E316 1CFCC986
   DC771138 3FC30AF9 CE28CA33 86D59E2C 8D72CE1E 7B4666E8
   y_qB =
   3289C4A3 A4FEE035 E39BDB88 5D509D22 4A142FF9 FBCC5CFE
   5CCBB302 68EE4748 7ED80448 58D31D84 8F7A95C6 35A347AC

   x_Z =
   04CC4FF3 DCCCB07A F24E0ACC 529955B3 6D7C8077 72B92FCB
   E48F3AFE 9A2F370A 1F98D3FA 73FD0C07 47C632E1 2F1423EC
   y_Z =
   7F465F90 BD69AFB8 F828A214 EB9716D6 6ABC59F1 7AF7C75E
   E7F1DE22 AB5D0508 5F5A01A9 382D05BF 72D96698 FE3FF64E





















Harkins                  Expires April 25, 2013                [Page 16]

Internet-Draft     Brainpool EC for IKE Group Registry      October 2012


A.6.  brainpoolP384t1

   dA =
   2B467652 35DB194F 4881C29A BB37D420 9C7FE86C 647CF364
   163C17E7 5845B895 50B9718C 0309E530 DB0738F5 81892497

   x_qA =
   7109CF92 F4A0A636 A99F9C99 869D7444 F1037DDB FF65FD11
   ECC89D48 D787FBEB 214502F7 51376C91 BA3B5A20 792FDB80
   y_qA =
   7FA86F26 F8E597B0 D5745376 0A82DBCC C9DAD227 B5100B55
   63E0C819 0C13CD03 1987AA44 17521A42 259AB0F0 7A563959

   dB =
   3AF21C86 309EA007 CD4EE4DF EE7E8BB2 6AA3D729 583F441C
   BA1F8560 B8977E92 12219E4A 310282A5 F749F815 ECAED238

   x_qB =
   3A2EEC09 537191F0 F1D6E32F CBFD2B73 7A3EBF3A A6635FA3
   B93996B9 FAE4EC5A 269FC5AA 45FD1E8A 087B0D44 75EBBB36
   y_qB =
   1E2BD825 64C92526 B71E317F 78E294EF 48C35835 909E903B
   85DD8F72 9B621700 5891ABEC 40D20DF3 B903485F 36A7130C

   x_Z =
   8246B430 31EC98A9 4634A476 D30FE994 6AF90CA8 E83AFFC0
   73BF63D4 70D023FE 7FDAD7A7 528021C7 F0CDD161 E7C49A95
   y_Z =
   20C0ECB8 486AC93A F1C7546A 1E85A922 A61EA191 FC2534E7
   E6FD496D C471ED5A AE2A0C3B A0356346 2303E1E3 DAD14160





















Harkins                  Expires April 25, 2013                [Page 17]

Internet-Draft     Brainpool EC for IKE Group Registry      October 2012


A.7.  brainpoolP512r1

   dA =
   636B6BE0 482A6C1C 41AA7AE7 B245E983 392DB94C ECEA2660
   A379CFE1 59559E35 75818253 91175FC1 95D28BAC 0CF03A78
   41A383B9 5C262B98 3782874C CE6FE333

   x_qA =
   0562E68B 9AF7CBFD 5565C6B1 6883B777 FF11C199 161ECC42
   7A39D17E C2166499 389571D6 A994977C 56AD8252 658BA8A1
   B72AE42F 4FB75321 51AFC3EF 0971CCDA
   y_qA =
   A7CA2D81 91E21776 A89860AF BC1F582F AA308D55 1C1DC613
   3AF9F9C3 CAD59998 D7007954 8140B90B 1F311AFB 378AA81F
   51B275B2 BE6B7DEE 978EFC73 43EA642E

   dB =
   0AF4E7F6 D52EDD52 907BB8DB AB3992A0 BB696EC1 0DF11892
   FF205B66 D381ECE7 2314E6A6 EA079CEA 06961DBA 5AE6422E
   F2E9EE80 3A1F236F B96A1799 B86E5C8B

   x_qB =
   5A7954E3 2663DFF1 1AE24712 D87419F2 6B708AC2 B92877D6
   BFEE2BFC 43714D89 BBDB6D24 D807BBD3 AEB7F0C3 25F862E8
   BADE4F74 636B97EA ACE739E1 1720D323
   y_qB =
   96D14621 A9283A1B ED84DE8D D64836B2 C0758B11 441179DC
   0C54C0D4 9A47C038 07D171DD 544B72CA AEF7B7CE 01C7753E
   2CAD1A86 1ECA55A7 1954EE1B A35E04BE

   x_Z =
   1EE8321A 4BBF93B9 CF8921AB 209850EC 9B7066D1 984EF08C
   2BB72323 6208AC8F 1A483E79 461A00E0 D5F6921C E9D36050
   2F85C812 BEDEE23A C5B210E5 811B191E
   y_Z =
   2632095B 7B936174 B41FD2FA F369B1D1 8DCADEED 7E410A7E
   251F0831 097C50D0 2CFED026 07B6A2D5 ADB4C000 60085622
   08631875 B58B54EC DA5A4F9F E9EAABA6













Harkins                  Expires April 25, 2013                [Page 18]

Internet-Draft     Brainpool EC for IKE Group Registry      October 2012


A.8.  brainpoolP512t1

   dA =
   3E3BF729 E3CD2EC3 B7D54B2F A1AF477C 142176B4 1CE73502
   5FE36439 3DAEAED6 504B0DAC 70364482 C0610250 AD79E319
   91EF374C A951F67D 59936953 DE77ED42

   x_qA =
   38774B48 4A807077 41725AC3 E13176D4 93F187F9 43979E3C
   DFAD1B48 E57ED0CA 6081D3C0 3B642158 AED16160 965F906F
   1314D243 5625B28D 7E6ADB79 21495502
   y_qA =
   47F956F7 2A95E6EB 5465F83D 4535A8BB 630121DE DFF907FD
   9EF33DBA 7516173D 784E047B FCF4A5AC 362F5431 93E8C305
   CB33D211 5007AF56 BAE9F4B1 08DCF3C6

   dB =
   43ACC620 4675EE0D 7ADC23BE E819CE21 BEB91916 6F6D8E23
   406EE8A2 53FFEFB9 83480DFD C7F92E43 9E4E9520 B13190A0
   72FDB588 EBCC9AC6 C8A8A7A9 4AA8EC9A

   x_qB =
   0417BFD5 D5440CE6 C1303BEE 23C8CDCD CCDC8AD1 91D54F15
   BF14C8D4 30D81485 75511E4E EDED8488 92330CBA 16D2BB20
   58116564 E4027755 730EDF80 E0202E9C
   y_qB =
   52E98A28 5F42F6DE CE35A2AC 5148284E B3F699B3 08E73B14
   C2969DB3 270F3E15 0FA61B69 454755C0 227F99E7 26FB6347
   B68C83E3 E1B605A0 8519933E A5B66CA2

   x_Z =
   8945201E 9F618412 D04EEA9F 04813321 A648EFB3 781810E9
   43E8FEEE A4E8144C B616F518 0EBF6CFF CC438A0E C67B4FEB
   348E2D02 A089D1FC DA166A6D 046C89BB
   y_Z =
   4A523725 4B206E78 EC7DC986 84146B39 BBF3ADAE CC12F252
   4EE6E6DA F7B76E3B 13E7180E 51C08481 BB3DFD78 07F99C7D
   F30C6C2F E199CCF4 85F2B557 96A3804B













Harkins                  Expires April 25, 2013                [Page 19]

Internet-Draft     Brainpool EC for IKE Group Registry      October 2012


Author's Address

   Dan Harkins (editor)
   Aruba Networks
   1322 Crossman avenue
   Sunnyvale, Californaia  94089
   United States of America

   Phone: +1 408 227 4500
   Email: dharkins@arubanetworks.com









































Harkins                  Expires April 25, 2013                [Page 20]


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