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Re: New 12288 and 16384 bit groups
Out of curiosity, are the primes currently in
draft-ietf-ipsec-ike-modp-groups-05 proven to be safe primes (of the form
N=2q+1, where q is prime), or just proven to be prime?
Trevor
At 01:10 AM 3/13/2003 +0200, Tero Kivinen wrote:
>Content-Transfer-Encoding: 7bit
>
>The 12288 bit group was fast to generate (only 13 days), the 16384 bit
>group took little longer (9.5 months), but finally they are here. Now
>you all can finally start using the full strength of the AES :-)
>
>Those primes have not been proven to be primes, only
>probabilistic tests have been done, and I do not intend to put
>them to draft-ietf-ipsec-ike-modp-groups-05. I would like to get
>them proven first, but that will probably take another year or
>so, provided that I can actually find windows machine running
>primo that stays stable for that long. I tried to prove the 12288
>bit group earlier, but every time the machine or the program
>crashed before it get very far (about two weeks or so).
>
>----------------------------------------------------------------------
>XXX. 12288-bit MODP Group
>
>This group is assigned id XXX.
>
>This prime is: 2^12288 - 2^12224 - 1 + 2^64 * { [2^12158 pi] + 7425765 }
>Its hexadecimal value is:
>
> FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
> 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
> EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
> E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
> EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
> C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
> 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
> 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
> E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
> DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
> 15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64
> ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7
> ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B
> F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
> BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31
> 43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7
> 88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA
> 2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
> 287C5947 4E6BC05D 99B2964F A090C3A2 233BA186 515BE7ED
> 1F612970 CEE2D7AF B81BDD76 2170481C D0069127 D5B05AA9
> 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492
> 36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD
> F8FF9406 AD9E530E E5DB382F 413001AE B06A53ED 9027D831
> 179727B0 865A8918 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B
> DB7F1447 E6CC254B 33205151 2BD7AF42 6FB8F401 378CD2BF
> 5983CA01 C64B92EC F032EA15 D1721D03 F482D7CE 6E74FEF6
> D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F BEC7E8F3
> 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
> CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328
> 06A1D58B B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C
> DA56C9EC 2EF29632 387FE8D7 6E3C0468 043E8F66 3F4860EE
> 12BF2D5B 0B7474D6 E694F91E 6DBE1159 74A3926F 12FEE5E4
> 38777CB6 A932DF8C D8BEC4D0 73B931BA 3BC832B6 8D9DD300
> 741FA7BF 8AFC47ED 2576F693 6BA42466 3AAB639C 5AE4F568
> 3423B474 2BF1C978 238F16CB E39D652D E3FDB8BE FC848AD9
> 22222E04 A4037C07 13EB57A8 1A23F0C7 3473FC64 6CEA306B
> 4BCBC886 2F8385DD FA9D4B7F A2C087E8 79683303 ED5BDD3A
> 062B3CF5 B3A278A6 6D2A13F8 3F44F82D DF310EE0 74AB6A36
> 4597E899 A0255DC1 64F31CC5 0846851D F9AB4819 5DED7EA1
> B1D510BD 7EE74D73 FAF36BC3 1ECFA268 359046F4 EB879F92
> 4009438B 481C6CD7 889A002E D5EE382B C9190DA6 FC026E47
> 9558E447 5677E9AA 9E3050E2 765694DF C81F56E8 80B96E71
> 60C980DD 98A573EA 4472065A 139CD290 6CD1CB72 9EC52A52
> 86D44014 A694CA45 7583D5CF EF26F1B9 0AD8291D A0799D00
> 022E9BED 55C6FA47 FCA5BB1A CA837645 6D98D948 79EE7E6D
> BFCD014B B1615599 14EC0B57 6A67E3E8 422E91E6 5BA141DA
> 92DE9C3A 6D6CCA51 36DD424B B1064988 EB5BA9AC 1269F7DF
> 673B982E 23FB6C99 BB2AA31C 5A6685FF D599149B 30AC67B8
> 464D80A9 5D42530A 681644D0 39060E8F 8FD52626 96D0A759
> 5AE3F935 A67DCFF5 A874A701 FBFA0C3D 534B4E39 BC095770
> 53374821 A11C3AC9 98E0BA71 8087B317 825A1ACF CFAEBBF2
> 4F25C605 1ADA9C28 5A1FCD61 14A838A1 ADE714C1 6A9401CD
> CF81E107 1FF7AB97 239F513B 15C5BCAE 2C0EB68D FC140303
> 7C0707C1 00802CFF EB833D46 8F2D5D2C 8960DE96 3702486F
> 746444FE 5F2A4BFD A50C91DC C8BD51C0 4EB97960 4DF0B6B7
> 322D5D8D 26BCF769 EA511851 83F400C3 BB3231CF A91D4790
> 788E3366 4EFA838B CCA02EE8 460FACCC 539522CE 13DB6E42
> 1BD08340 FD82812F CB2E04A4 0925DF1E 559E6C1C AF2BE26B
> F7A69DC7 F664C204 2CE2EB84 B733CFCB 95449C87 CB9ADC49
> 1406B779 A7E13361 DE9611C6 1D023685 EF27E6AF 3A52DF63
> 3B1EBB0E B6E1477E 98C250D9 B11930F4 BBC70611 CC857642
> 3750CECD C930AE85 84A85350 CA997114 54250000 84CEB937
> 5C77FE27 840C5395 606B1DF5 97C44666 C10D55BC 75E8F1DA
> CF04460E D6492942 7CA3F9BB 666DCDE2 FFFFFFFF FFFFFFFF
>
>The generator is: 2.
>
>
>XXX. 16384-bit MODP Group
>
>This group is assigned id XXX.
>
>This prime is: 2^16384 - 2^16320 - 1 + 2^64 * { [2^16254 pi] + 50814484 }
>Its hexadecimal value is:
>
> FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
> 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
> EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
> E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
> EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D
> C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F
> 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
> 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B
> E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9
> DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510
> 15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64
> ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7
> ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B
> F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
> BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31
> 43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7
> 88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA
> 2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
> 287C5947 4E6BC05D 99B2964F A090C3A2 233BA186 515BE7ED
> 1F612970 CEE2D7AF B81BDD76 2170481C D0069127 D5B05AA9
> 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492
> 36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD
> F8FF9406 AD9E530E E5DB382F 413001AE B06A53ED 9027D831
> 179727B0 865A8918 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B
> DB7F1447 E6CC254B 33205151 2BD7AF42 6FB8F401 378CD2BF
> 5983CA01 C64B92EC F032EA15 D1721D03 F482D7CE 6E74FEF6
> D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F BEC7E8F3
> 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
> CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328
> 06A1D58B B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C
> DA56C9EC 2EF29632 387FE8D7 6E3C0468 043E8F66 3F4860EE
> 12BF2D5B 0B7474D6 E694F91E 6DBE1159 74A3926F 12FEE5E4
> 38777CB6 A932DF8C D8BEC4D0 73B931BA 3BC832B6 8D9DD300
> 741FA7BF 8AFC47ED 2576F693 6BA42466 3AAB639C 5AE4F568
> 3423B474 2BF1C978 238F16CB E39D652D E3FDB8BE FC848AD9
> 22222E04 A4037C07 13EB57A8 1A23F0C7 3473FC64 6CEA306B
> 4BCBC886 2F8385DD FA9D4B7F A2C087E8 79683303 ED5BDD3A
> 062B3CF5 B3A278A6 6D2A13F8 3F44F82D DF310EE0 74AB6A36
> 4597E899 A0255DC1 64F31CC5 0846851D F9AB4819 5DED7EA1
> B1D510BD 7EE74D73 FAF36BC3 1ECFA268 359046F4 EB879F92
> 4009438B 481C6CD7 889A002E D5EE382B C9190DA6 FC026E47
> 9558E447 5677E9AA 9E3050E2 765694DF C81F56E8 80B96E71
> 60C980DD 98A573EA 4472065A 139CD290 6CD1CB72 9EC52A52
> 86D44014 A694CA45 7583D5CF EF26F1B9 0AD8291D A0799D00
> 022E9BED 55C6FA47 FCA5BB1A CA837645 6D98D948 79EE7E6D
> BFCD014B B1615599 14EC0B57 6A67E3E8 422E91E6 5BA141DA
> 92DE9C3A 6D6CCA51 36DD424B B1064988 EB5BA9AC 1269F7DF
> 673B982E 23FB6C99 BB2AA31C 5A6685FF D599149B 30AC67B8
> 464D80A9 5D42530A 681644D0 39060E8F 8FD52626 96D0A759
> 5AE3F935 A67DCFF5 A874A701 FBFA0C3D 534B4E39 BC095770
> 53374821 A11C3AC9 98E0BA71 8087B317 825A1ACF CFAEBBF2
> 4F25C605 1ADA9C28 5A1FCD61 14A838A1 ADE714C1 6A9401CD
> CF81E107 1FF7AB97 239F513B 15C5BCAE 2C0EB68D FC140303
> 7C0707C1 00802CFF EB833D46 8F2D5D2C 8960DE96 3702486F
> 746444FE 5F2A4BFD A50C91DC C8BD51C0 4EB97960 4DF0B6B7
> 322D5D8D 26BCF769 EA511851 83F400C3 BB3231CF A91D4790
> 788E3366 4EFA838B CCA02EE8 460FACCC 539522CE 13DB6E42
> 1BD08340 FD82812F CB2E04A4 0925DF1E 559E6C1C AF2BE26B
> F7A69DC7 F664C204 2CE2EB84 B733CFCB 95449C87 CB9ADC49
> 1406B779 A7E13361 DE9611C6 1D023685 EF27E6AF 3A52DF63
> 3B1EBB0E B6E1477E 98C250D9 B11930F4 BBC70611 CC857642
> 3750CECD C930AE85 84A85350 CA997114 54250000 84CEB937
> 5C77FE27 840C5395 606B1DF5 97C44666 C10D55BC 75E8F1DA
> CF04460E D6492942 7CA3F9BB 65FC7EFE A7AEAFCB 07854F1B
> A1B8D15C 3ABA5BEC 61839782 968F8AAC DDC7F9C7 138F41BE
> 8A59772E 6679C743 E00FA275 9499B209 4B93325E 27042CDA
> B18543AE A538BA9E 297F0F14 C7828B7D 3CBDD3A9 CD874ACF
> 464E4983 C6709E58 1488E9C2 3DC4C4AD BAEB7F9B BAB0C7D9
> B8EF1165 699EF220 EC5FCDF4 40633FCA 30CCB77B EF9B16A9
> 59560861 5A2AE600 BBB3A943 F6CBE54E CABBDF6B 56DB8BE1
> 05486D8A 0A41D85C 3B3751DD 5867C544 04F32A0C 3AD86F65
> 80CD3F87 AA80D8F3 ED5CD724 131C288E 7567A782 F2EAB785
> 3BB321AF 18188B29 E72AD72A ECBCE11B 9922C7AB C66F7C32
> A808DA6E 5956AED4 101A168C 8F0AAD2C CC67BA75 70086E3D
> E6D502C6 61D7E826 657DE65F 988F5F6A 3E0DE226 A5F8CB5D
> C47B64D7 C59A04A0 438D620A 71F987F5 A5B7B7E8 5E162EA6
> 55FD6129 46C89C98 E6E0F0FF C6B091A5 B36CC2BA D4CB8C15
> 23F65239 1B6F0C4A 163AFCBB CD31BFFA BF8A3B58 7B9F0F1C
> D7528536 7A192DF8 D0841745 080F84F8 117BB8AD A8EAAAFA
> B6DB13C5 7EB2D3F4 31D0BD10 BBDAAEED 5953CEC7 50734841
> 76079E67 A1A15371 F912D1DA 8F605894 33D8A87C 96E34991
> BF2220E8 3071EDA8 DFC54930 DA72DD24 91E12282 D5A4ACA1
> 4256EFC0 2B465227 4518AC5D 08E08380 1610A34A 83157D7A
> 876B7D0F 88CFDC18 4CDCBC24 A364DF90 7597FB3C 5B088EF6
> DF378DD6 72FB9D18 10217CA9 F39DCC9B A981E021 0985723A
> FFFFFFFF FFFFFFFF
>
>The generator is: 2.
>--
>kivinen@ssh.fi
>SSH Communications Security http://www.ssh.fi/
>SSH IPSEC Toolkit http://www.ssh.fi/ipsec/