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 groupsfor 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. . . . . . . . . . . . . . . . . . . . . . . 22. 1536-bit MODP Group . . . . . . . . . . . . . . . . . . . 33. 2048-bit MODP Group . . . . . . . . . . . . . . . . . . . 34. 3072-bit MODP Group . . . . . . . . . . . . . . . . . . . 45. 4096-bit MODP Group . . . . . . . . . . . . . . . . . . . 56. 6144-bit MODP Group . . . . . . . . . . . . . . . . . . . 67. 8192-bit MODP Group . . . . . . . . . . . . . . . . . . . 68. Security Considerations . . . . . . . . . . . . . . . . . 89. IANA Considerations . . . . . . . . . . . . . . . . . . . 810. Normative References. . . . . . . . . . . . . . . . . . . 811. Non-Normative References. . . . . . . . . . . . . . . . . 812. Authors' Addresses . . . . . . . . . . . . . . . . . . . 913. Full Copyright Statement. . . . . . . . . . . . . . . . . 10Kivinen & Kojo Standards Track [Page 1]
RFC 3526 MODP Diffie-Hellman groups for IKE May 20031. 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 20032. 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 20034. 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 20038. 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", RFC2412, 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.html12. 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 200313. Full Copyright Statement
Copyright (C) The Internet Society (2003). All Rights Reserved.
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Acknowledgement
Funding for the RFC Editor function is currently provided by the
Internet Society.
Kivinen & Kojo Standards Track [Page 10]
