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diff --git a/doc/ikev2/[RFC3526] - More Modular Exponential (MODP) Diffie-Hellman groups for Internet Key Exchange (IKE).txt b/doc/ikev2/[RFC3526] - More Modular Exponential (MODP) Diffie-Hellman groups for Internet Key Exchange (IKE).txt deleted file mode 100644 index 7b688a33f..000000000 --- a/doc/ikev2/[RFC3526] - More Modular Exponential (MODP) Diffie-Hellman groups for Internet Key Exchange (IKE).txt +++ /dev/null @@ -1,563 +0,0 @@ - - - - - - -Network Working Group T. Kivinen -Request for Comments: 3526 M. Kojo -Category: Standards Track SSH Communications Security - May 2003 - - - More Modular Exponential (MODP) Diffie-Hellman groups - for Internet Key Exchange (IKE) - -Status of this Memo - - This document specifies an Internet standards track protocol for the - Internet community, and requests discussion and suggestions for - improvements. Please refer to the current edition of the "Internet - Official Protocol Standards" (STD 1) for the standardization state - and status of this protocol. Distribution of this memo is unlimited. - -Copyright Notice - - Copyright (C) The Internet Society (2003). All Rights Reserved. - -Abstract - - This document defines new Modular Exponential (MODP) Groups for the - Internet Key Exchange (IKE) protocol. It documents the well known - and used 1536 bit group 5, and also defines new 2048, 3072, 4096, - 6144, and 8192 bit Diffie-Hellman groups numbered starting at 14. - The selection of the primes for theses groups follows the criteria - established by Richard Schroeppel. - -Table of Contents - - 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . 2 - 2. 1536-bit MODP Group . . . . . . . . . . . . . . . . . . . 3 - 3. 2048-bit MODP Group . . . . . . . . . . . . . . . . . . . 3 - 4. 3072-bit MODP Group . . . . . . . . . . . . . . . . . . . 4 - 5. 4096-bit MODP Group . . . . . . . . . . . . . . . . . . . 5 - 6. 6144-bit MODP Group . . . . . . . . . . . . . . . . . . . 6 - 7. 8192-bit MODP Group . . . . . . . . . . . . . . . . . . . 6 - 8. Security Considerations . . . . . . . . . . . . . . . . . 8 - 9. IANA Considerations . . . . . . . . . . . . . . . . . . . 8 - 10. Normative References. . . . . . . . . . . . . . . . . . . 8 - 11. Non-Normative References. . . . . . . . . . . . . . . . . 8 - 12. Authors' Addresses . . . . . . . . . . . . . . . . . . . 9 - 13. Full Copyright Statement. . . . . . . . . . . . . . . . . 10 - - - - - - -Kivinen & Kojo Standards Track [Page 1] - -RFC 3526 MODP Diffie-Hellman groups for IKE May 2003 - - -1. Introduction - - One of the important protocol parameters negotiated by Internet Key - Exchange (IKE) [RFC-2409] is the Diffie-Hellman "group" that will be - used for certain cryptographic operations. IKE currently defines 4 - groups. These groups are approximately as strong as a symmetric key - of 70-80 bits. - - The new Advanced Encryption Standard (AES) cipher [AES], which has - more strength, needs stronger groups. For the 128-bit AES we need - about a 3200-bit group [Orman01]. The 192 and 256-bit keys would - need groups that are about 8000 and 15400 bits respectively. Another - source [RSA13] [Rousseau00] estimates that the security equivalent - key size for the 192-bit symmetric cipher is 2500 bits instead of - 8000 bits, and the equivalent key size 256-bit symmetric cipher is - 4200 bits instead of 15400 bits. - - Because of this disagreement, we just specify different groups - without specifying which group should be used with 128, 192 or 256- - bit AES. With current hardware groups bigger than 8192-bits being - too slow for practical use, this document does not provide any groups - bigger than 8192-bits. - - The exponent size used in the Diffie-Hellman must be selected so that - it matches other parts of the system. It should not be the weakest - link in the security system. It should have double the entropy of - the strength of the entire system, i.e., if you use a group whose - strength is 128 bits, you must use more than 256 bits of randomness - in the exponent used in the Diffie-Hellman calculation. - - - - - - - - - - - - - - - - - - - - - - -Kivinen & Kojo Standards Track [Page 2] - -RFC 3526 MODP Diffie-Hellman groups for IKE May 2003 - - -2. 1536-bit MODP Group - - The 1536 bit MODP group has been used for the implementations for - quite a long time, but was not defined in RFC 2409 (IKE). - Implementations have been using group 5 to designate this group, we - standardize that practice here. - - The prime is: 2^1536 - 2^1472 - 1 + 2^64 * { [2^1406 pi] + 741804 } - - 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 CA237327 FFFFFFFF FFFFFFFF - - The generator is: 2. - -3. 2048-bit MODP Group - - This group is assigned id 14. - - This prime is: 2^2048 - 2^1984 - 1 + 2^64 * { [2^1918 pi] + 124476 } - - 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 8AACAA68 FFFFFFFF FFFFFFFF - - The generator is: 2. - - - - - - - - -Kivinen & Kojo Standards Track [Page 3] - -RFC 3526 MODP Diffie-Hellman groups for IKE May 2003 - - -4. 3072-bit MODP Group - - This group is assigned id 15. - - This prime is: 2^3072 - 2^3008 - 1 + 2^64 * { [2^2942 pi] + 1690314 } - - 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 A93AD2CA FFFFFFFF FFFFFFFF - - The generator is: 2. - - - - - - - - - - - - - - - - - - - - - - - - - -Kivinen & Kojo Standards Track [Page 4] - -RFC 3526 MODP Diffie-Hellman groups for IKE May 2003 - - -5. 4096-bit MODP Group - - This group is assigned id 16. - - This prime is: 2^4096 - 2^4032 - 1 + 2^64 * { [2^3966 pi] + 240904 } - - 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 34063199 - FFFFFFFF FFFFFFFF - - The generator is: 2. - - - - - - - - - - - - - - - - - - - -Kivinen & Kojo Standards Track [Page 5] - -RFC 3526 MODP Diffie-Hellman groups for IKE May 2003 - - -6. 6144-bit MODP Group - - This group is assigned id 17. - - This prime is: 2^6144 - 2^6080 - 1 + 2^64 * { [2^6014 pi] + 929484 } - - 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 - 6DCC4024 FFFFFFFF FFFFFFFF - - The generator is: 2. - -7. 8192-bit MODP Group - - This group is assigned id 18. - - This prime is: 2^8192 - 2^8128 - 1 + 2^64 * { [2^8062 pi] + 4743158 } - - - - - - - -Kivinen & Kojo Standards Track [Page 6] - -RFC 3526 MODP Diffie-Hellman groups for IKE May 2003 - - - 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 98EDD3DF FFFFFFFF FFFFFFFF - - The generator is: 2. - - - - -Kivinen & Kojo Standards Track [Page 7] - -RFC 3526 MODP Diffie-Hellman groups for IKE May 2003 - - -8. Security Considerations - - This document describes new stronger groups to be used in IKE. The - strengths of the groups defined here are always estimates and there - are as many methods to estimate them as there are cryptographers. - For the strength estimates below we took the both ends of the scale - so the actual strength estimate is likely between the two numbers - given here. - - +--------+----------+---------------------+---------------------+ - | Group | Modulus | Strength Estimate 1 | Strength Estimate 2 | - | | +----------+----------+----------+----------+ - | | | | exponent | | exponent | - | | | in bits | size | in bits | size | - +--------+----------+----------+----------+----------+----------+ - | 5 | 1536-bit | 90 | 180- | 120 | 240- | - | 14 | 2048-bit | 110 | 220- | 160 | 320- | - | 15 | 3072-bit | 130 | 260- | 210 | 420- | - | 16 | 4096-bit | 150 | 300- | 240 | 480- | - | 17 | 6144-bit | 170 | 340- | 270 | 540- | - | 18 | 8192-bit | 190 | 380- | 310 | 620- | - +--------+----------+---------------------+---------------------+ - -9. IANA Considerations - - IKE [RFC-2409] defines 4 Diffie-Hellman Groups, numbered 1 through 4. - - This document defines a new group 5, and new groups from 14 to 18. - Requests for additional assignment are via "IETF Consensus" as - defined in RFC 2434 [RFC-2434]. Specifically, new groups are - expected to be documented in a Standards Track RFC. - -10. Normative References - - [RFC-2409] Harkins, D. and D. Carrel, "The Internet Key Exchange - (IKE)", RFC 2409, November 1998. - - [RFC-2434] Narten, T. and H. Alvestrand, "Guidelines for Writing an - IANA Considerations Section in RFCs", BCP 26, RFC 2434, - October 1998. - -11. Non-Normative References - - [AES] NIST, FIPS PUB 197, "Advanced Encryption Standard - (AES)," November 2001. - http://csrc.nist.gov/publications/fips/fips197/fips- - 197.{ps,pdf} - - - - -Kivinen & Kojo Standards Track [Page 8] - -RFC 3526 MODP Diffie-Hellman groups for IKE May 2003 - - - [RFC-2412] Orman, H., "The OAKLEY Key Determination Protocol", RFC - 2412, November 1998. - - [Orman01] Orman, H. and P. Hoffman, "Determining Strengths For - Public Keys Used For Exchanging Symmetric Keys", Work in - progress. - - [RSA13] Silverman, R. "RSA Bulleting #13: A Cost-Based Security - Analysis of Symmetric and Asymmetric Key Lengths", April - 2000, http://www.rsasecurity.com/rsalabs/bulletins/ - bulletin13.html - - [Rousseau00] Rousseau, F. "New Time and Space Based Key Size - Equivalents for RSA and Diffie-Hellman", December 2000, - http://www.sandelman.ottawa.on.ca/ipsec/2000/12/ - msg00045.html - -12. Authors' Addresses - - Tero Kivinen - SSH Communications Security Corp - Fredrikinkatu 42 - FIN-00100 HELSINKI - Finland - - EMail: kivinen@ssh.fi - - - Mika Kojo - HELSINKI - Finland - - EMail: mika.kojo@helsinki.fi - - - - - - - - - - - - - - - - - - -Kivinen & Kojo Standards Track [Page 9] - -RFC 3526 MODP Diffie-Hellman groups for IKE May 2003 - - -13. Full Copyright Statement - - Copyright (C) The Internet Society (2003). All Rights Reserved. - - This document and translations of it may be copied and furnished to - others, and derivative works that comment on or otherwise explain it - or assist in its implementation may be prepared, copied, published - and distributed, in whole or in part, without restriction of any - kind, provided that the above copyright notice and this paragraph are - included on all such copies and derivative works. However, this - document itself may not be modified in any way, such as by removing - the copyright notice or references to the Internet Society or other - Internet organizations, except as needed for the purpose of - developing Internet standards in which case the procedures for - copyrights defined in the Internet Standards process must be - followed, or as required to translate it into languages other than - English. - - The limited permissions granted above are perpetual and will not be - revoked by the Internet Society or its successors or assigns. - - This document and the information contained herein is provided on an - "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING - TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING - BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION - HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF - MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. - -Acknowledgement - - Funding for the RFC Editor function is currently provided by the - Internet Society. - - - - - - - - - - - - - - - - - - - -Kivinen & Kojo Standards Track [Page 10] - |