Subject: New 12288 and 16384 bit groups

From: Tero Kivinen <[email-masked]>
Date: Thu, 13 Mar 2003 01:10:48 +0200

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.
-- 
[email-masked]
SSH Communications Security                  http://www.ssh.fi/
SSH IPSEC Toolkit                            http://www.ssh.fi/ipsec/

---

From: Trevor Perrin <[email-masked]>
Date: Thu, 13 Mar 2003 16:18:16 -0800

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
>

---

From: Tero Kivinen <[email-masked]>
Date: Sat, 15 Mar 2003 21:44:58 +0200

> N=2q+1, where q is prime), or just proven to be prime?

All the groups in the draft-ietf-ipsec-ike-modp-groups-05 are proven
to be safe primes (i.e both the p and the (p - 1) / 2 are proven to be
prime). The ECPP/primo certificates can be found at
http://ftp.ssh.com/pub/ietf/ecpp-certificates/ (that url used to be in
the draft, but was removed because url's are not stable enough to be
used as references (that url is going to be stable :-)). 
-- 
[email-masked]
SSH Communications Security                  http://www.ssh.fi/
SSH IPSEC Toolkit                            http://www.ssh.fi/ipsec/

---

From: Alan Barrett <[email-masked]>
Date: Mon, 17 Mar 2003 11:08:40 +0200

> used as references (that url is going to be stable :-)). 

Perhaps the IANA or the RFC Editor (or both) would be willing to keep
stable copies of supporting documentation that's too large (or otherwise
inconvenient) for inclusion in an RFC.

If so, then I'd suggest keeping the "ftp.ssh.com" URL in the draft, with a
note saying that it should be changed to an "iana.org" or "rfc-editor.org"
URL before publication as an RFC.

--apb (Alan Barrett)

---

From: Trevor Perrin <[email-masked]>
Date: Mon, 17 Mar 2003 12:26:26 -0800

>URL before publication as an RFC.

And even if not, maybe the draft could have a note that the primes are 
proven to be safe primes, and that certificates do exist (and if there was 
a website with links to them, with keywords like "IKE primes" and "ECPP 
certificates", they'd turn up on google easily enough)..

Trevor