doc/ikev2/[RFC3526] - More Modular Exponential (MODP) Diffie-Hellman groups for Internet Key Exchange (IKE).txt

   1
   2
   3
   4
   5
   6
   7 Network Working Group                                         T. Kivinen
   8 Request for Comments: 3526                                       M. Kojo
   9 Category: Standards Track                    SSH Communications Security
  10                                                                 May 2003
  11
  12
  13          More Modular Exponential (MODP) Diffie-Hellman groups
  14                     for Internet Key Exchange (IKE)
  15
  16 Status of this Memo
  17
  18    This document specifies an Internet standards track protocol for the
  19    Internet community, and requests discussion and suggestions for
  20    improvements.  Please refer to the current edition of the "Internet
  21    Official Protocol Standards" (STD 1) for the standardization state
  22    and status of this protocol.  Distribution of this memo is unlimited.
  23
  24 Copyright Notice
  25
  26    Copyright (C) The Internet Society (2003).  All Rights Reserved.
  27
  28 Abstract
  29
  30    This document defines new Modular Exponential (MODP) Groups for the
  31    Internet Key Exchange (IKE) protocol.  It documents the well known
  32    and used 1536 bit group 5, and also defines new 2048, 3072, 4096,
  33    6144, and 8192 bit Diffie-Hellman groups numbered starting at 14.
  34    The selection of the primes for theses groups follows the criteria
  35    established by Richard Schroeppel.
  36
  37 Table of Contents
  38
  39    1.   Introduction. . . . . . . . . . . . . . . . . . . . . . .  2
  40    2.   1536-bit MODP Group . . . . . . . . . . . . . . . . . . .  3
  41    3.   2048-bit MODP Group . . . . . . . . . . . . . . . . . . .  3
  42    4.   3072-bit MODP Group . . . . . . . . . . . . . . . . . . .  4
  43    5.   4096-bit MODP Group . . . . . . . . . . . . . . . . . . .  5
  44    6.   6144-bit MODP Group . . . . . . . . . . . . . . . . . . .  6
  45    7.   8192-bit MODP Group . . . . . . . . . . . . . . . . . . .  6
  46    8.   Security Considerations . . . . . . . . . . . . . . . . .  8
  47    9.   IANA Considerations . . . . . . . . . . . . . . . . . . .  8
  48    10.  Normative References. . . . . . . . . . . . . . . . . . .  8
  49    11.  Non-Normative References. . . . . . . . . . . . . . . . .  8
  50    12.  Authors' Addresses  . . . . . . . . . . . . . . . . . . .  9
  51    13.  Full Copyright Statement. . . . . . . . . . . . . . . . . 10
  52
  53
  54
  55
  56
  57
  58 Kivinen & Kojo              Standards Track                     [Page 1]
  59 \f
  60 RFC 3526           MODP Diffie-Hellman groups for IKE           May 2003
  61
  62
  63 1.  Introduction
  64
  65    One of the important protocol parameters negotiated by Internet Key
  66    Exchange (IKE) [RFC-2409] is the Diffie-Hellman "group" that will be
  67    used for certain cryptographic operations.  IKE currently defines 4
  68    groups.  These groups are approximately as strong as a symmetric key
  69    of 70-80 bits.
  70
  71    The new Advanced Encryption Standard (AES) cipher [AES], which has
  72    more strength, needs stronger groups.  For the 128-bit AES we need
  73    about a 3200-bit group [Orman01].  The 192 and 256-bit keys would
  74    need groups that are about 8000 and 15400 bits respectively.  Another
  75    source [RSA13] [Rousseau00] estimates that the security equivalent
  76    key size for the 192-bit symmetric cipher is 2500 bits instead of
  77    8000 bits, and the equivalent key size 256-bit symmetric cipher is
  78    4200 bits instead of 15400 bits.
  79
  80    Because of this disagreement, we just specify different groups
  81    without specifying which group should be used with 128, 192 or 256-
  82    bit AES.  With current hardware groups bigger than 8192-bits being
  83    too slow for practical use, this document does not provide any groups
  84    bigger than 8192-bits.
  85
  86    The exponent size used in the Diffie-Hellman must be selected so that
  87    it matches other parts of the system.  It should not be the weakest
  88    link in the security system.  It should have double the entropy of
  89    the strength of the entire system, i.e., if you use a group whose
  90    strength is 128 bits, you must use more than 256 bits of randomness
  91    in the exponent used in the Diffie-Hellman calculation.
  92
  93
  94
  95
  96
  97
  98
  99
 100
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114 Kivinen & Kojo              Standards Track                     [Page 2]
 115 \f
 116 RFC 3526           MODP Diffie-Hellman groups for IKE           May 2003
 117
 118
 119 2.  1536-bit MODP Group
 120
 121    The 1536 bit MODP group has been used for the implementations for
 122    quite a long time, but was not defined in RFC 2409 (IKE).
 123    Implementations have been using group 5 to designate this group, we
 124    standardize that practice here.
 125
 126    The prime is: 2^1536 - 2^1472 - 1 + 2^64 * { [2^1406 pi] + 741804 }
 127
 128    Its hexadecimal value is:
 129
 130       FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
 131       29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
 132       EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
 133       E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
 134       EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
 135       C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
 136       83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
 137       670C354E 4ABC9804 F1746C08 CA237327 FFFFFFFF FFFFFFFF
 138
 139    The generator is: 2.
 140
 141 3.  2048-bit MODP Group
 142
 143    This group is assigned id 14.
 144
 145    This prime is: 2^2048 - 2^1984 - 1 + 2^64 * { [2^1918 pi] + 124476 }
 146
 147    Its hexadecimal value is:
 148
 149       FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
 150       29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
 151       EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
 152       E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
 153       EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
 154       C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
 155       83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
 156       670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
 157       E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
 158       DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
 159       15728E5A 8AACAA68 FFFFFFFF FFFFFFFF
 160
 161    The generator is: 2.
 162
 163
 164
 165
 166
 167
 168
 169
 170 Kivinen & Kojo              Standards Track                     [Page 3]
 171 \f
 172 RFC 3526           MODP Diffie-Hellman groups for IKE           May 2003
 173
 174
 175 4.  3072-bit MODP Group
 176
 177    This group is assigned id 15.
 178
 179    This prime is: 2^3072 - 2^3008 - 1 + 2^64 * { [2^2942 pi] + 1690314 }
 180
 181    Its hexadecimal value is:
 182
 183       FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
 184       29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
 185       EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
 186       E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
 187       EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
 188       C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
 189       83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
 190       670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
 191       E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
 192       DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
 193       15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64
 194       ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7
 195       ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B
 196       F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
 197       BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31
 198       43DB5BFC E0FD108E 4B82D120 A93AD2CA FFFFFFFF FFFFFFFF
 199
 200    The generator is: 2.
 201
 202
 203
 204
 205
 206
 207
 208
 209
 210
 211
 212
 213
 214
 215
 216
 217
 218
 219
 220
 221
 222
 223
 224
 225
 226 Kivinen & Kojo              Standards Track                     [Page 4]
 227 \f
 228 RFC 3526           MODP Diffie-Hellman groups for IKE           May 2003
 229
 230
 231 5.  4096-bit MODP Group
 232
 233    This group is assigned id 16.
 234
 235    This prime is: 2^4096 - 2^4032 - 1 + 2^64 * { [2^3966 pi] + 240904 }
 236
 237    Its hexadecimal value is:
 238
 239       FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
 240       29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
 241       EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
 242       E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
 243       EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
 244       C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
 245       83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
 246       670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
 247       E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
 248       DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
 249       15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64
 250       ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7
 251       ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B
 252       F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
 253       BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31
 254       43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7
 255       88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA
 256       2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
 257       287C5947 4E6BC05D 99B2964F A090C3A2 233BA186 515BE7ED
 258       1F612970 CEE2D7AF B81BDD76 2170481C D0069127 D5B05AA9
 259       93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34063199
 260       FFFFFFFF FFFFFFFF
 261
 262    The generator is: 2.
 263
 264
 265
 266
 267
 268
 269
 270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282 Kivinen & Kojo              Standards Track                     [Page 5]
 283 \f
 284 RFC 3526           MODP Diffie-Hellman groups for IKE           May 2003
 285
 286
 287 6.  6144-bit MODP Group
 288
 289    This group is assigned id 17.
 290
 291    This prime is: 2^6144 - 2^6080 - 1 + 2^64 * { [2^6014 pi] + 929484 }
 292
 293    Its hexadecimal value is:
 294
 295    FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08
 296    8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B
 297    302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9
 298    A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6
 299    49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
 300    FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
 301    670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
 302    180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
 303    3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
 304    04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
 305    B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
 306    1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
 307    BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
 308    E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26
 309    99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBBBC2DB
 310    04DE8EF9 2E8EFC14 1FBECAA6 287C5947 4E6BC05D 99B2964F A090C3A2
 311    233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127
 312    D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492
 313    36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD F8FF9406
 314    AD9E530E E5DB382F 413001AE B06A53ED 9027D831 179727B0 865A8918
 315    DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B DB7F1447 E6CC254B 33205151
 316    2BD7AF42 6FB8F401 378CD2BF 5983CA01 C64B92EC F032EA15 D1721D03
 317    F482D7CE 6E74FEF6 D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F
 318    BEC7E8F3 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
 319    CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328 06A1D58B
 320    B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C DA56C9EC 2EF29632
 321    387FE8D7 6E3C0468 043E8F66 3F4860EE 12BF2D5B 0B7474D6 E694F91E
 322    6DCC4024 FFFFFFFF FFFFFFFF
 323
 324    The generator is: 2.
 325
 326 7.  8192-bit MODP Group
 327
 328    This group is assigned id 18.
 329
 330    This prime is: 2^8192 - 2^8128 - 1 + 2^64 * { [2^8062 pi] + 4743158 }
 331
 332
 333
 334
 335
 336
 337
 338 Kivinen & Kojo              Standards Track                     [Page 6]
 339 \f
 340 RFC 3526           MODP Diffie-Hellman groups for IKE           May 2003
 341
 342
 343    Its hexadecimal value is:
 344
 345       FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
 346       29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
 347       EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
 348       E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
 349       EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
 350       C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
 351       83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
 352       670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
 353       E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
 354       DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
 355       15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64
 356       ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7
 357       ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B
 358       F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
 359       BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31
 360       43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7
 361       88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA
 362       2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
 363       287C5947 4E6BC05D 99B2964F A090C3A2 233BA186 515BE7ED
 364       1F612970 CEE2D7AF B81BDD76 2170481C D0069127 D5B05AA9
 365       93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492
 366       36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD
 367       F8FF9406 AD9E530E E5DB382F 413001AE B06A53ED 9027D831
 368       179727B0 865A8918 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B
 369       DB7F1447 E6CC254B 33205151 2BD7AF42 6FB8F401 378CD2BF
 370       5983CA01 C64B92EC F032EA15 D1721D03 F482D7CE 6E74FEF6
 371       D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F BEC7E8F3
 372       23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
 373       CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328
 374       06A1D58B B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C
 375       DA56C9EC 2EF29632 387FE8D7 6E3C0468 043E8F66 3F4860EE
 376       12BF2D5B 0B7474D6 E694F91E 6DBE1159 74A3926F 12FEE5E4
 377       38777CB6 A932DF8C D8BEC4D0 73B931BA 3BC832B6 8D9DD300
 378       741FA7BF 8AFC47ED 2576F693 6BA42466 3AAB639C 5AE4F568
 379       3423B474 2BF1C978 238F16CB E39D652D E3FDB8BE FC848AD9
 380       22222E04 A4037C07 13EB57A8 1A23F0C7 3473FC64 6CEA306B
 381       4BCBC886 2F8385DD FA9D4B7F A2C087E8 79683303 ED5BDD3A
 382       062B3CF5 B3A278A6 6D2A13F8 3F44F82D DF310EE0 74AB6A36
 383       4597E899 A0255DC1 64F31CC5 0846851D F9AB4819 5DED7EA1
 384       B1D510BD 7EE74D73 FAF36BC3 1ECFA268 359046F4 EB879F92
 385       4009438B 481C6CD7 889A002E D5EE382B C9190DA6 FC026E47
 386       9558E447 5677E9AA 9E3050E2 765694DF C81F56E8 80B96E71
 387       60C980DD 98EDD3DF FFFFFFFF FFFFFFFF
 388
 389    The generator is: 2.
 390
 391
 392
 393
 394 Kivinen & Kojo              Standards Track                     [Page 7]
 395 \f
 396 RFC 3526           MODP Diffie-Hellman groups for IKE           May 2003
 397
 398
 399 8.  Security Considerations
 400
 401    This document describes new stronger groups to be used in IKE.  The
 402    strengths of the groups defined here are always estimates and there
 403    are as many methods to estimate them as there are cryptographers.
 404    For the strength estimates below we took the both ends of the scale
 405    so the actual strength estimate is likely between the two numbers
 406    given here.
 407
 408    +--------+----------+---------------------+---------------------+
 409    | Group  | Modulus  | Strength Estimate 1 | Strength Estimate 2 |
 410    |        |          +----------+----------+----------+----------+
 411    |        |          |          | exponent |          | exponent |
 412    |        |          | in bits  | size     | in bits  | size     |
 413    +--------+----------+----------+----------+----------+----------+
 414    |   5    | 1536-bit |       90 |     180- |      120 |     240- |
 415    |  14    | 2048-bit |      110 |     220- |      160 |     320- |
 416    |  15    | 3072-bit |      130 |     260- |      210 |     420- |
 417    |  16    | 4096-bit |      150 |     300- |      240 |     480- |
 418    |  17    | 6144-bit |      170 |     340- |      270 |     540- |
 419    |  18    | 8192-bit |      190 |     380- |      310 |     620- |
 420    +--------+----------+---------------------+---------------------+
 421
 422 9.  IANA Considerations
 423
 424    IKE [RFC-2409] defines 4 Diffie-Hellman Groups, numbered 1 through 4.
 425
 426    This document defines a new group 5, and new groups from 14 to 18.
 427    Requests for additional assignment are via "IETF Consensus" as
 428    defined in RFC 2434 [RFC-2434].  Specifically, new groups are
 429    expected to be documented in a Standards Track RFC.
 430
 431 10.  Normative References
 432
 433    [RFC-2409]   Harkins, D. and D. Carrel, "The Internet Key Exchange
 434                 (IKE)", RFC 2409, November 1998.
 435
 436    [RFC-2434]   Narten, T. and H. Alvestrand, "Guidelines for Writing an
 437                 IANA Considerations Section in RFCs", BCP 26, RFC 2434,
 438                 October 1998.
 439
 440 11.  Non-Normative References
 441
 442    [AES]        NIST, FIPS PUB 197, "Advanced Encryption Standard
 443                 (AES)," November 2001.
 444                 http://csrc.nist.gov/publications/fips/fips197/fips-
 445                 197.{ps,pdf}
 446
 447
 448
 449
 450 Kivinen & Kojo              Standards Track                     [Page 8]
 451 \f
 452 RFC 3526           MODP Diffie-Hellman groups for IKE           May 2003
 453
 454
 455    [RFC-2412]   Orman, H., "The OAKLEY Key Determination Protocol", RFC
 456                 2412, November 1998.
 457
 458    [Orman01]    Orman, H. and P. Hoffman, "Determining Strengths For
 459                 Public Keys Used For Exchanging Symmetric Keys", Work in
 460                 progress.
 461
 462    [RSA13]      Silverman, R. "RSA Bulleting #13: A Cost-Based Security
 463                 Analysis of Symmetric and Asymmetric Key Lengths", April
 464                 2000, http://www.rsasecurity.com/rsalabs/bulletins/
 465                 bulletin13.html
 466
 467    [Rousseau00] Rousseau, F. "New Time and Space Based Key Size
 468                 Equivalents for RSA and Diffie-Hellman", December 2000,
 469                 http://www.sandelman.ottawa.on.ca/ipsec/2000/12/
 470                 msg00045.html
 471
 472 12.  Authors' Addresses
 473
 474    Tero Kivinen
 475    SSH Communications Security Corp
 476    Fredrikinkatu 42
 477    FIN-00100 HELSINKI
 478    Finland
 479
 480    EMail: kivinen@ssh.fi
 481
 482
 483    Mika Kojo
 484    HELSINKI
 485    Finland
 486
 487    EMail: mika.kojo@helsinki.fi
 488
 489
 490
 491
 492
 493
 494
 495
 496
 497
 498
 499
 500
 501
 502
 503
 504
 505
 506 Kivinen & Kojo              Standards Track                     [Page 9]
 507 \f
 508 RFC 3526           MODP Diffie-Hellman groups for IKE           May 2003
 509
 510
 511 13.  Full Copyright Statement
 512
 513    Copyright (C) The Internet Society (2003).  All Rights Reserved.
 514
 515    This document and translations of it may be copied and furnished to
 516    others, and derivative works that comment on or otherwise explain it
 517    or assist in its implementation may be prepared, copied, published
 518    and distributed, in whole or in part, without restriction of any
 519    kind, provided that the above copyright notice and this paragraph are
 520    included on all such copies and derivative works.  However, this
 521    document itself may not be modified in any way, such as by removing
 522    the copyright notice or references to the Internet Society or other
 523    Internet organizations, except as needed for the purpose of
 524    developing Internet standards in which case the procedures for
 525    copyrights defined in the Internet Standards process must be
 526    followed, or as required to translate it into languages other than
 527    English.
 528
 529    The limited permissions granted above are perpetual and will not be
 530    revoked by the Internet Society or its successors or assigns.
 531
 532    This document and the information contained herein is provided on an
 533    "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING
 534    TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING
 535    BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION
 536    HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF
 537    MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
 538
 539 Acknowledgement
 540
 541    Funding for the RFC Editor function is currently provided by the
 542    Internet Society.
 543
 544
 545
 546
 547
 548
 549
 550
 551
 552
 553
 554
 555
 556
 557
 558
 559
 560
 561
 562 Kivinen & Kojo              Standards Track                    [Page 10]
 563 \f