RFC 3526 - More Modular Exponential (MODP) Diffie-Hellman groups
RFC 3526 - More Modular Exponential (MODP) Diffie-Hellman groups
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Network Working Group
T. Kivinen
Request for Comments: 3526
Category: Standards Track
SSH Communications Security
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.
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 , 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
Introduction. . . . . . . . . . . . . . . . . . . . . . .
1536-bit MODP Group . . . . . . . . . . . . . . . . . . .
2048-bit MODP Group . . . . . . . . . . . . . . . . . . .
3072-bit MODP Group . . . . . . . . . . . . . . . . . . .
4096-bit MODP Group . . . . . . . . . . . . . . . . . . .
6144-bit MODP Group . . . . . . . . . . . . . . . . . . .
8192-bit MODP Group . . . . . . . . . . . . . . . . . . .
Security Considerations . . . . . . . . . . . . . . . . .
IANA Considerations . . . . . . . . . . . . . . . . . . .
Normative References. . . . . . . . . . . . . . . . . . .
Non-Normative References. . . . . . . . . . . . . . . . .
Authors' Addresses
. . . . . . . . . . . . . . . . . . .
Full Copyright Statement. . . . . . . . . . . . . . . . . 10
Introduction
One of the important protocol parameters negotiated by Internet Key
Exchange (IKE) [] is the Diffie-Hellman "group" that will be
used for certain cryptographic operations.
IKE currently defines 4
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.
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-
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.
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
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 CCD1
A67CC74 020BBEA6 3B139B22 514A4DD
EF9519B3 CD3A431B 302B0A6D F25F56D 6D51C245
E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
EE386BFB 5A899FA5 AE9FB1FE6
C3BF05 98DAD39A 69163FA8 FD24CF5F
83655D23 DCA3AD96 1C62F356 208552BB 9ED6D
670C354E 4ABCC08 CA237327 FFFFFFFF FFFFFFFF
The generator is: 2.
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 CCD1
A67CC74 020BBEA6 3B139B22 514A4DD
EF9519B3 CD3A431B 302B0A6D F25F56D 6D51C245
E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
EE386BFB 5A899FA5 AE9FB1FE6
C3BF05 98DAD39A 69163FA8 FD24CF5F
83655D23 DCA3AD96 1C62F356 208552BB 9ED6D
670C354E 4ABCC08 CA1E46 2E36CE3B
E39E772C 180E3A2 EC07A28F B5C55DF0 6F4C52C9
DE2BCBF6 5497C EA956AE5 15D10
AACAA68 FFFFFFFF FFFFFFFF
The generator is: 2.
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 CCD1
A67CC74 020BBEA6 3B139B22 514A4DD
EF9519B3 CD3A431B 302B0A6D F25F56D 6D51C245
E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
EE386BFB 5A899FA5 AE9FB1FE6
C3BF05 98DAD39A 69163FA8 FD24CF5F
83655D23 DCA3AD96 1C62F356 208552BB 9ED6D
670C354E 4ABCC08 CA1E46 2E36CE3B
E39E772C 180E3A2 EC07A28F B5C55DF0 6F4C52C9
DE2BCBF6 5497C EA956AE5 15D10
AAAC42D AD3A33 A85521AB DF1CBA64
ECFB8504 58DBEF0A 8AEAC7D BE1E4C7
ABF5AE8C DBE8C94E0 4A25619D CEE3D226 1AD2EE6B
F12FFA06 D98A3 3EC86A64 521F2B18 177B200C
BAD946E2 08E24FA0 74E5AB31
43DB5BFC E0FD108E 4B82D120 A93AD2CA FFFFFFFF FFFFFFFF
The generator is: 2.
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 CCD1
A67CC74 020BBEA6 3B139B22 514A4DD
EF9519B3 CD3A431B 302B0A6D F25F56D 6D51C245
E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
EE386BFB 5A899FA5 AE9FB1FE6
C3BF05 98DAD39A 69163FA8 FD24CF5F
83655D23 DCA3AD96 1C62F356 208552BB 9ED6D
670C354E 4ABCC08 CA1E46 2E36CE3B
E39E772C 180E3A2 EC07A28F B5C55DF0 6F4C52C9
DE2BCBF6 5497C EA956AE5 15D10
AAAC42D AD3A33 A85521AB DF1CBA64
ECFB8504 58DBEF0A 8AEAC7D BE1E4C7
ABF5AE8C DBE8C94E0 4A25619D CEE3D226 1AD2EE6B
F12FFA06 D98A3 3EC86A64 521F2B18 177B200C
BAD946E2 08E24FA0 74E5AB31
43DB5BFC E0FD108E 4B82D120 AA723C12 A787E6D7
88719A10 BDBA5B26 99CE23C 1A50BDA
2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
287CBC05D 99B2964F A090C3A2 233BA186 515BE7ED
1F612970 CEE2D7AF B81BDD76 2170481C DB05AA9
93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9
FFFFFFFF FFFFFFFF
The generator is: 2.
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 CCD1 29024E08
8A67CC74 020BBEA6 3B139B22 514A4DD EF9519B3 CD3A431B
302B0A6D F25F56D 6D51C245 E485B576 625E7EC6 F44C42E9
A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9FB1FE6
ECE45B3D C3BF05 98DAD39A 69163FA8
FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED6D
670C354E 4ABCC08 CA1E46 2E36CE3B E39E772C
180E3A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6
3995497C EA956AE5 15D10 AAAC42D AD33170D
521AB DF1CBA64 ECFB8504 58DBEF0A 8AEAC7D
BE1E4C7 ABF5AE8C DBE8C94E0 4A25619D CEE3D226
1AD2EE6B F12FFA06 D98A3 3EC86A64 521F2B18 177B200C
BAD946E2 08E24FA0 74E5AB31 43DB5BFC
E0FD108E 4B82D120 AA723C12 A787E6D7 88719A10 BDBA5B26
99CE23C 1A50BDA 2583E9CA 2AD44CE8 DBBBC2DB
04DE8EF9 2E8EFC14 1FBECAA6 287CBC05D 99B2964F A090C3A2
233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127
D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9
36C3FAB4 D27CDCB2 602646DE CDBA37BD F8FF9406
AD9E530E E5DB382F 413001AE B06A53ED 727B0 865A8918
DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B DB7F4B
2BD7AF42 6FB8F401 378CD2BF B92EC F032EA15 D1721D03
F482D7CE 6E74FEF6 D55E702F AC9E 59E7C97F
BEC7E8F3 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
CC8F6D7E BF48E1D8 14CC5ED2 0F715EE F29BE328 06A1D58B
B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C DA56C9EC 2EF29632
387FE8D7 6E3CF66 3F4860EE 12BF2D5B 0B4F91E
6DCC4024 FFFFFFFF FFFFFFFF
The generator is: 2.
8192-bit MODP Group
This group is assigned id 18.
This prime is: 2^8192 - 2^8128 - 1 + 2^64 * { [2^8062 pi] + 4743158 }
Its hexadecimal value is:
FFFFFFFF FFFFFFFF C90FDAA2 CCD1
A67CC74 020BBEA6 3B139B22 514A4DD
EF9519B3 CD3A431B 302B0A6D F25F56D 6D51C245
E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
EE386BFB 5A899FA5 AE9FB1FE6
C3BF05 98DAD39A 69163FA8 FD24CF5F
83655D23 DCA3AD96 1C62F356 208552BB 9ED6D
670C354E 4ABCC08 CA1E46 2E36CE3B
E39E772C 180E3A2 EC07A28F B5C55DF0 6F4C52C9
DE2BCBF6 5497C EA956AE5 15D10
AAAC42D AD3A33 A85521AB DF1CBA64
ECFB8504 58DBEF0A 8AEAC7D BE1E4C7
ABF5AE8C DBE8C94E0 4A25619D CEE3D226 1AD2EE6B
F12FFA06 D98A3 3EC86A64 521F2B18 177B200C
BAD946E2 08E24FA0 74E5AB31
43DB5BFC E0FD108E 4B82D120 AA723C12 A787E6D7
88719A10 BDBA5B26 99CE23C 1A50BDA
2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
287CBC05D 99B2964F A090C3A2 233BA186 515BE7ED
1F612970 CEE2D7AF B81BDD76 2170481C DB05AA9
93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9
36C3FAB4 D27CDCB2 602646DE CDBA37BD
F8FF9406 AD9E530E E5DB382F 413001AE B06A53ED
865A8918 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B
DB7F4B BD7AF42 6FB8F401 378CD2BF
B92EC F032EA15 D2D7CE 6E74FEF6
D55E702F AC9E 59E7C97F BEC7E8F3
23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
CC8F6D7E BF48E1D8 14CC5ED2 0F715EE F29BE328
06A1D58B B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C
DA56C9EC 2EFFE8D7 6E3CF66 3F4860EE
12BF2D5B 0B4F91E 6DBE6F 12FEE5E4
32DF8C D8BEC4D0 73B931BA 3BC832B6 8D9DD300
741FA7BF 8AFC47ED BA42466 3AAB639C 5AE4F568
BF1C978 238F16CB E39D652D E3FDB8BE FC848AD9
37C07 13EB57A8 1A23F0C7 CEA306B
4BCBC886 2F8385DD FA9D4B7F A2C087E8
062B3CF5 B3A278A6 6D2A13F8 3F44F82D DF310EE0 74AB6A36
55DC1 64F31CC5 0846851D F9AB4819 5DED7EA1
B1D510BD 7EE74D73 FAF36BC3 1ECFA268
1C6CD7 889A002E D5EE382B C9190DA6 FC026E47
7E9AA 9E694DF C81F56E8 80B96E71
60C980DD 98EDD3DF FFFFFFFF FFFFFFFF
The generator is: 2.
Security Considerations
This document describes new stronger groups to be used in IKE.
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.
+--------+----------+---------------------+---------------------+
| Strength Estimate 1 | Strength Estimate 2 |
+----------+----------+----------+----------+
| exponent |
| exponent |
+--------+----------+----------+----------+----------+----------+
| 1536-bit |
| 2048-bit |
| 3072-bit |
| 4096-bit |
| 6144-bit |
| 8192-bit |
+--------+----------+---------------------+---------------------+
IANA Considerations
IKE [] 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
Specifically, new groups are
expected to be documented in a Standards Track RFC.
Normative References
Harkins, D. and D. Carrel, "The Internet Key Exchange
(IKE)", , November 1998.
Narten, T. and H. Alvestrand, "Guidelines for Writing an
IANA Considerations Section in RFCs", BCP 26, ,
October 1998.
Non-Normative References
NIST, FIPS PUB 197, "Advanced Encryption Standard
(AES)," November 2001.
197.{ps,pdf}
Orman, H., "The OAKLEY Key Determination Protocol", RFC
2412, November 1998.
Orman, H. and P. Hoffman, "Determining Strengths For
Public Keys Used For Exchanging Symmetric Keys", Work in
Silverman, R. "RSA Bulleting #13: A Cost-Based Security
Analysis of Symmetric and Asymmetric Key Lengths", April
bulletin13.html
[Rousseau00] Rousseau, F. "New Time and Space Based Key Size
Equivalents for RSA and Diffie-Hellman", December 2000,
msg00045.html
Authors' Addresses
Tero Kivinen
SSH Communications Security Corp
Fredrikinkatu 42
FIN-00100 HELSINKI
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《蜡笔小新 第1季》影视原声IP Security Protocol Working Group (IPSEC)
T. Kivinen
INTERNET-DRAFT
and M. Kojo
SSH Communications Security
Expires: 19 May 2002
19 November 2001
More MODP Diffie-Hellman groups for IKE
Status of This Memo
This document is a submission to the IETF IP Security Protocol
(IPSEC) Working Group.
Comments are solicited and should be
addressed to the working group mailing list (ipsec@lists.tislabs.com)
or to the editor.
This document is an Internet-Draft and is in full conformance
with all provisions of .
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF), its areas, and its working groups.
other groups may also distribute working documents as
Internet-Drafts.
Internet-Drafts are draft documents valid for a maximum of six
months and may be updated, replaced, or obsoleted by other
documents at any time.
It is inappropriate to use Internet-
Drafts as reference material or to cite them other than as
"work in progress."
The list of current Internet-Drafts can be accessed at
The list of Internet-Draft Shadow Directories can be accessed at
This document defines new MODP groups for the IKE [] protocol.
It documents the well know and used 1536 bit group 5, and also defines
new , , and 8192 bit Diffie-Hellman groups. The
selection of the primes for theses groups follows the criteria estab-
lished by Richard Schroeppel as described in [].
. Kivinen, et. al.
INTERNET-DRAFT
19 November 2001
Table of Contents
Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . .
Specification of Requirements
. . . . . . . . . . . . . . . . .
1536-bit MODP Group
. . . . . . . . . . . . . . . . . . . . . .
2048-bit MODP Group
. . . . . . . . . . . . . . . . . . . . . .
3072-bit MODP Group
. . . . . . . . . . . . . . . . . . . . . .
4096-bit MODP Group
. . . . . . . . . . . . . . . . . . . . . .
6144-bit MODP Group
. . . . . . . . . . . . . . . . . . . . . .
8192-bit MODP Group
. . . . . . . . . . . . . . . . . . . . . .
Security Considerations
. . . . . . . . . . . . . . . . . . . .
References
. . . . . . . . . . . . . . . . . . . . . . . . . .
Authors' Addresses
. . . . . . . . . . . . . . . . . . . . . .
Introduction
Current Diffie-Hellman groups defined in the IKE [] have only
strength that matches strength of symmetric key of 70-80 bits. The new
AES cipher needs stronger groups. For the 128-bit AES we need about
2000-bit group. The 192 and 256-bit keys would need groups that are
about 9000 and 15000 bits respectively. Another source estimates that
the security equivalent key size for the 192-bit symmetric cipher is
bits instead of 9000 bits, and the equivalent key size 256-bit
symmetric cipher is 4200 bits instead of 15000 bits.
Because of this disagreement this document just specifies different
groups without specifying which group should be using 128, 192 or
256-bit AES. In the current hardware groups bigger than 8192-bits are
too slow for practical use, thus this document does not provide any
groups bigger than 8192-bits.
Also the exponent size used in the Diffie-Hellman must be selected so
that it matches other parts of the system. The exponent size should be
selected so that it is not the weakest link in the security system,
meaning that it should be at least the double of the estimated strength
of selected group. I.e if you use group whose strength is 128 bits, you
must use more than 256 bits of randomness in the exponent used in the
Diffie-Hellman calculation.
Specification of Requirements
This document shall use the keywords "MUST", "MUST NOT", "REQUIRED",
"SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED, "MAY", and
"OPTIONAL" to describe requirements. They are to be interpreted as
described in [] document.
1536-bit MODP Group
The 1536 bit MODP group has been used for the implementations for quite
a long time, but it has not been documented in the current RFCs or
drafts. This group has already been used as having group id 5.
. Kivinen, et. al.
INTERNET-DRAFT
19 November 2001
The prime is: 2^1536 - 2^1472 - 1 + 2^64 * { [2^1406 pi] + 741804 }
Its hexadecimal value is
FFFFFFFF FFFFFFFF C90FDAA2 CCD1
A67CC74 020BBEA6 3B139B22 514A4DD
EF9519B3 CD3A431B 302B0A6D F25F56D 6D51C245
E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
EE386BFB 5A899FA5 AE9FB1FE6
C3BF05 98DAD39A 69163FA8 FD24CF5F
83655D23 DCA3AD96 1C62F356 208552BB 9ED6D
670C354E 4ABCC08 CA237327 FFFFFFFF FFFFFFFF
The generator is: 2.
2048-bit MODP Group
This group is assigned id XX.
This prime is: 2^2048 - 2^1984 - 1 + 2^64 * { [2^1918 pi] + 124476 }
Its hexadecimal value is
FFFFFFFF FFFFFFFF C90FDAA2 CCD1
A67CC74 020BBEA6 3B139B22 514A4DD
EF9519B3 CD3A431B 302B0A6D F25F56D 6D51C245
E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
EE386BFB 5A899FA5 AE9FB1FE6
C3BF05 98DAD39A 69163FA8 FD24CF5F
83655D23 DCA3AD96 1C62F356 208552BB 9ED6D
670C354E 4ABCC08 CA1E46 2E36CE3B
E39E772C 180E3A2 EC07A28F B5C55DF0 6F4C52C9
DE2BCBF6 5497C EA956AE5 15D10
AACAA68 FFFFFFFF FFFFFFFF
The generator is: 2.
3072-bit MODP Group
This group is assigned id XX + 1.
This prime is: 2^3072 - 2^3008 - 1 + 2^64 * { [2^2942 pi] + 1690314 }
Its hexadecimal value is
FFFFFFFF FFFFFFFF C90FDAA2 CCD1
A67CC74 020BBEA6 3B139B22 514A4DD
EF9519B3 CD3A431B 302B0A6D F25F56D 6D51C245
E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
EE386BFB 5A899FA5 AE9FB1FE6
C3BF05 98DAD39A 69163FA8 FD24CF5F
83655D23 DCA3AD96 1C62F356 208552BB 9ED6D
670C354E 4ABCC08 CA1E46 2E36CE3B
E39E772C 180E3A2 EC07A28F B5C55DF0 6F4C52C9
DE2BCBF6 5497C EA956AE5 15D10
AAAC42D AD3A33 A85521AB DF1CBA64
ECFB8504 58DBEF0A 8AEAC7D BE1E4C7
. Kivinen, et. al.
INTERNET-DRAFT
19 November 2001
ABF5AE8C DBE8C94E0 4A25619D CEE3D226 1AD2EE6B
F12FFA06 D98A3 3EC86A64 521F2B18 177B200C
BAD946E2 08E24FA0 74E5AB31
43DB5BFC E0FD108E 4B82D120 A93AD2CA FFFFFFFF FFFFFFFF
The generator is: 2.
4096-bit MODP Group
This group is assigned id XX + 2.
This prime is: 2^4096 - 2^4032 - 1 + 2^64 * { [2^3966 pi] + 240904 }
Its hexadecimal value is
FFFFFFFF FFFFFFFF C90FDAA2 CCD1
A67CC74 020BBEA6 3B139B22 514A4DD
EF9519B3 CD3A431B 302B0A6D F25F56D 6D51C245
E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
EE386BFB 5A899FA5 AE9FB1FE6
C3BF05 98DAD39A 69163FA8 FD24CF5F
83655D23 DCA3AD96 1C62F356 208552BB 9ED6D
670C354E 4ABCC08 CA1E46 2E36CE3B
E39E772C 180E3A2 EC07A28F B5C55DF0 6F4C52C9
DE2BCBF6 5497C EA956AE5 15D10
AAAC42D AD3A33 A85521AB DF1CBA64
ECFB8504 58DBEF0A 8AEAC7D BE1E4C7
ABF5AE8C DBE8C94E0 4A25619D CEE3D226 1AD2EE6B
F12FFA06 D98A3 3EC86A64 521F2B18 177B200C
BAD946E2 08E24FA0 74E5AB31
43DB5BFC E0FD108E 4B82D120 AA723C12 A787E6D7
88719A10 BDBA5B26 99CE23C 1A50BDA
2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
287CBC05D 99B2964F A090C3A2 233BA186 515BE7ED
1F612970 CEE2D7AF B81BDD76 2170481C DB05AA9
93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9
FFFFFFFF FFFFFFFF
The generator is: 2.
6144-bit MODP Group
This group is assigned id XX + 3.
This prime is: 2^6144 - 2^6080 - 1 + 2^64 * { [2^6014 pi] + 929484 }
Its hexadecimal value is
FFFFFFFF FFFFFFFF C90FDAA2 CCD1
A67CC74 020BBEA6 3B139B22 514A4DD
EF9519B3 CD3A431B 302B0A6D F25F56D 6D51C245
E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
EE386BFB 5A899FA5 AE9FB1FE6
C3BF05 98DAD39A 69163FA8 FD24CF5F
83655D23 DCA3AD96 1C62F356 208552BB 9ED6D
. Kivinen, et. al.
INTERNET-DRAFT
19 November 2001
670C354E 4ABCC08 CA1E46 2E36CE3B
E39E772C 180E3A2 EC07A28F B5C55DF0 6F4C52C9
DE2BCBF6 5497C EA956AE5 15D10
AAAC42D AD3A33 A85521AB DF1CBA64
ECFB8504 58DBEF0A 8AEAC7D BE1E4C7
ABF5AE8C DBE8C94E0 4A25619D CEE3D226 1AD2EE6B
F12FFA06 D98A3 3EC86A64 521F2B18 177B200C
BAD946E2 08E24FA0 74E5AB31
43DB5BFC E0FD108E 4B82D120 AA723C12 A787E6D7
88719A10 BDBA5B26 99CE23C 1A50BDA
2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
287CBC05D 99B2964F A090C3A2 233BA186 515BE7ED
1F612970 CEE2D7AF B81BDD76 2170481C DB05AA9
93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9
36C3FAB4 D27CDCB2 602646DE CDBA37BD
F8FF9406 AD9E530E E5DB382F 413001AE B06A53ED
865A8918 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B
DB7F4B BD7AF42 6FB8F401 378CD2BF
B92EC F032EA15 D2D7CE 6E74FEF6
D55E702F AC9E 59E7C97F BEC7E8F3
23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
CC8F6D7E BF48E1D8 14CC5ED2 0F715EE F29BE328
06A1D58B B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C
DA56C9EC 2EFFE8D7 6E3CF66 3F4860EE
12BF2D5B 0B4F91E 6DCC4024 FFFFFFFF FFFFFFFF
The generator is: 2.
8192-bit MODP Group
This group is assigned id XX + 4.
This prime is: 2^8192 - 2^8128 - 1 + 2^64 * { [2^8062 pi] + 4743158 }
Its hexadecimal value is
FFFFFFFF FFFFFFFF C90FDAA2 CCD1
A67CC74 020BBEA6 3B139B22 514A4DD
EF9519B3 CD3A431B 302B0A6D F25F56D 6D51C245
E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
EE386BFB 5A899FA5 AE9FB1FE6
C3BF05 98DAD39A 69163FA8 FD24CF5F
83655D23 DCA3AD96 1C62F356 208552BB 9ED6D
670C354E 4ABCC08 CA1E46 2E36CE3B
E39E772C 180E3A2 EC07A28F B5C55DF0 6F4C52C9
DE2BCBF6 5497C EA956AE5 15D10
AAAC42D AD3A33 A85521AB DF1CBA64
ECFB8504 58DBEF0A 8AEAC7D BE1E4C7
ABF5AE8C DBE8C94E0 4A25619D CEE3D226 1AD2EE6B
F12FFA06 D98A3 3EC86A64 521F2B18 177B200C
BAD946E2 08E24FA0 74E5AB31
43DB5BFC E0FD108E 4B82D120 AA723C12 A787E6D7
88719A10 BDBA5B26 99CE23C 1A50BDA
2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6
. Kivinen, et. al.
INTERNET-DRAFT
19 November 2001
287CBC05D 99B2964F A090C3A2 233BA186 515BE7ED
1F612970 CEE2D7AF B81BDD76 2170481C DB05AA9
93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9
36C3FAB4 D27CDCB2 602646DE CDBA37BD
F8FF9406 AD9E530E E5DB382F 413001AE B06A53ED
865A8918 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B
DB7F4B BD7AF42 6FB8F401 378CD2BF
B92EC F032EA15 D2D7CE 6E74FEF6
D55E702F AC9E 59E7C97F BEC7E8F3
23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
CC8F6D7E BF48E1D8 14CC5ED2 0F715EE F29BE328
06A1D58B B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C
DA56C9EC 2EFFE8D7 6E3CF66 3F4860EE
12BF2D5B 0B4F91E 6DBE6F 12FEE5E4
32DF8C D8BEC4D0 73B931BA 3BC832B6 8D9DD300
741FA7BF 8AFC47ED BA42466 3AAB639C 5AE4F568
BF1C978 238F16CB E39D652D E3FDB8BE FC848AD9
37C07 13EB57A8 1A23F0C7 CEA306B
4BCBC886 2F8385DD FA9D4B7F A2C087E8
062B3CF5 B3A278A6 6D2A13F8 3F44F82D DF310EE0 74AB6A36
55DC1 64F31CC5 0846851D F9AB4819 5DED7EA1
B1D510BD 7EE74D73 FAF36BC3 1ECFA268
1C6CD7 889A002E D5EE382B C9190DA6 FC026E47
7E9AA 9E694DF C81F56E8 80B96E71
60C980DD 98EDD3DF FFFFFFFF FFFFFFFF
The generator is: 2.
Security Considerations
This document describes new stronger groups to be used in the IKE. The
strengths of the groups defined here is always an estimate 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 can be between those two numbers given here.
The strength of the 1536-bit group is believed to be between 90 and 120
bits. The exponent size for this group should be more than 180 - 220
The strength of the 2048-bit group is believed to be between 110 and 160
bits. The exponent size for this group should be more than 220 - 320
The strength of the 3072-bit group is believed to be between 130 and 210
bits. The exponent size for this group should be more than 260 - 420
The strength of the 4096-bit group is believed to be between 150 and 240
bits. The exponent size for this group should be more than 300 - 480
The strength of the 6144-bit group is believed to be between 170 and 270
bits. The exponent size for this group should be more than 340 - 540
. Kivinen, et. al.
INTERNET-DRAFT
19 November 2001
The strength of the 8192-bit group is believed to be between 190 and 310
bits. The exponent size for this group should be more than 380 - 620
ECPP certificats for ,
and 6144 bit groups can be
found from the . The
generation of the 8192-bit group certificate is still in progress and if
and when it is ready it will be put to the same place.
References
[] Orman H., "The OAKLEY Key Determination Protocol", November
[] Harkins D., Carrel D., "The Internet Key Exchange (IKE)",
November 1998
[] Bradner, S., "Key words for use in RFCs to indicate
Requirement Levels", March 1997
Authors' Addresses
Tero Kivinen
SSH Communications Security Corp
Fredrikinkatu 42
FIN-00100 HELSINKI
E-mail: kivinen@ssh.fi
E-mail: mrskojo@cc.helsinki.fi
. Kivinen, et. al.
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