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.
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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.
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
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 }
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.
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.
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
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