Network Working Group                                         T. Kivinen
Request for Comments: 3526                                       M. Kojo
Category: Standards Track                    SSH Communications Security
                                                                May 2003
        
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)

用于Internet密钥交换(IKE)的更多模指数(MODP)Diffie-Hellman组

Status of this Memo

本备忘录的状况

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.

本文件规定了互联网社区的互联网标准跟踪协议,并要求进行讨论和提出改进建议。有关本协议的标准化状态和状态,请参考当前版本的“互联网官方协议标准”(STD 1)。本备忘录的分发不受限制。

Copyright Notice

版权公告

Copyright (C) The Internet Society (2003). All Rights Reserved.

版权所有(C)互联网协会(2003年)。版权所有。

Abstract

摘要

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.

本文档为Internet密钥交换(IKE)协议定义了新的模块化指数(MODP)组。它记录了已知和使用的1536位组5,还定义了编号从14开始的新2048、3072、4096、6144和8192位Diffie-Hellman组。这些组的素数选择遵循Richard Schroeppel制定的标准。

Table of Contents

目录

   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
        
   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
        
1. Introduction
1. 介绍

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.

互联网密钥交换(IKE)[RFC-2409]协商的重要协议参数之一是Diffie-Hellman“组”,用于某些加密操作。IKE目前定义了4个组。这些组的强度大约相当于70-80位的对称密钥。

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.

新的高级加密标准(AES)密码[AES]具有更强的强度,需要更强的组。对于128位AES,我们需要大约3200位组[Orman01]。192位和256位密钥将需要分别约为8000位和15400位的组。另一来源[RSA13][Rousseau00]估计,192位对称密码的安全等效密钥大小是2500位而不是8000位,256位对称密码的等效密钥大小是4200位而不是15400位。

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.

由于这种分歧,我们只指定了不同的组,而没有指定哪个组应与128、192或256位AES一起使用。由于当前大于8192位的硬件组的实际使用速度太慢,本文档不提供任何大于8192位的组。

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.

必须选择Diffie Hellman中使用的指数大小,以便它与系统的其他部分匹配。它不应该是安全系统中最薄弱的环节。它应该具有整个系统强度的两倍熵,即,如果使用强度为128位的组,则在Diffie-Hellman计算中使用的指数中必须使用256位以上的随机性。

2. 1536-bit MODP Group
2. 1536位MODP组

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.

1536位MODP组用于实现已有相当长的时间,但在RFC 2409(IKE)中没有定义。实现一直使用组5来指定这个组,我们在这里标准化了这种做法。

   The prime is: 2^1536 - 2^1472 - 1 + 2^64 * { [2^1406 pi] + 741804 }
        
   The prime is: 2^1536 - 2^1472 - 1 + 2^64 * { [2^1406 pi] + 741804 }
        

Its hexadecimal value is:

其十六进制值为:

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

FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED EE386B5A899FA5 AE9F2411 7C4B16 49286651 45B3 6D C20078 A16305 BF4565655CFD36粪便1C62F356 208552BB 9ED52907 7096966D 670C354E 4ABC9804 F1746C08 CA237327 FFFFFFFFFFFF

The generator is: 2.

发电机是:2。

3. 2048-bit MODP Group
3. 2048位MODP组

This group is assigned id 14.

此组被分配了id 14。

   This prime is: 2^2048 - 2^1984 - 1 + 2^64 * { [2^1918 pi] + 124476 }
        
   This prime is: 2^2048 - 2^1984 - 1 + 2^64 * { [2^1918 pi] + 124476 }
        

Its hexadecimal value is:

其十六进制值为:

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

FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED EE386B5A899FA5 AE9F2411 7C4B16 49286651 45B3 6D C20078 A16305 BF4565655CFD36粪便1C62F356 208552BB 9ED52907 7096966D 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AACAA68 FFFFFFFFFFFFFF

The generator is: 2.

发电机是:2。

4. 3072-bit MODP Group
4. 3072位MODP组

This group is assigned id 15.

此组被分配了id 15。

   This prime is: 2^3072 - 2^3008 - 1 + 2^64 * { [2^2942 pi] + 1690314 }
        
   This prime is: 2^3072 - 2^3008 - 1 + 2^64 * { [2^2942 pi] + 1690314 }
        

Its hexadecimal value is:

其十六进制值为:

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

FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED EE386B5A899FA5 AE9F2411 7C4B16 49286651 45B3 6D C20078 A16305 BF4565655CFD36粪便1C62F356 208552BB 9ED52907 7096966D 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2EC3B E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D 04507A33 A521AB DF1BA64 ECFB850A 8B5F5A 8AE157 5D0607E40A 8E407E408AEC 197E407E40C 8AEC9DCEE3D226 1AD26B F12FFA006 D98A0864 D8760273 3EC86A64 521F2B18 177B200C BBE11757 7A615D6C 770988C0 BAD946E208E24FA0 74E5AB31 43DB5BFC E0FD108E 4B82D120 A93AD2CA FFFFFFFFFF

The generator is: 2.

发电机是:2。

5. 4096-bit MODP Group
5. 4096位MODP组

This group is assigned id 16.

此组被分配了id 16。

   This prime is: 2^4096 - 2^4032 - 1 + 2^64 * { [2^3966 pi] + 240904 }
        
   This prime is: 2^4096 - 2^4032 - 1 + 2^64 * { [2^3966 pi] + 240904 }
        

Its hexadecimal value is:

其十六进制值为:

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

FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED EE386B5A899FA5 AE9F2411 7C4B16 49286651 45B3 6D C20078 A16305 BF4565655CFD36粪便1C62F356 208552BB 9ED52907 7096966D 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2EC3B E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D 04507A33 A521AB DF1BA64 ECFB850A 8B5F5A 8AE157 5D0607E40A 8E407E408AEC 197E407E40C 8AEC9DCEE3D226 1AD26B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C BBE1757 7A615D6C 77098C0 BAD946E208E24FA0 74E5AB31 43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBC2DB 04DE8EFC18 2EBC16 287C5947B965BFC1861F612970 CEE2D7AF B81BDD76 21704811C D0069127 D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34063199 FFFFFFFFFFFFFF

The generator is: 2.

发电机是:2。

6. 6144-bit MODP Group
6. 6144位MODP组

This group is assigned id 17.

该组被分配了id 17。

   This prime is: 2^6144 - 2^6080 - 1 + 2^64 * { [2^6014 pi] + 929484 }
        
   This prime is: 2^6144 - 2^6080 - 1 + 2^64 * { [2^6014 pi] + 929484 }
        

Its hexadecimal value is:

其十六进制值为:

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

FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED EE386B5A899FA5 AE9F2411 7C4B16 49286651 45B3 6D C20078 A16305 BF4565655CFD36粪便1C62F356 208552BB 9ED52907 7096966D 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2EC3B E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D 04507A33 A521AB DF1BA64 ECFB850A 8B5F5A 8AE157 5D0607E40A 8E407E408AEC 197E407E40C 8AEC9DCEE3D226 1AD26B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C BBE1757 7A615D6C 77098C0 BAD946E208E24FA0 74E5AB31 43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBC2DB 04DE8EFC18 2EBC16 287C5947B965BFC1861F612970 CEE2D7AF B81BDD76 21704811C D0069127 D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492 36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD FF9406 AD9E530E E538DB382F 413001AE B06A553ED 9027D831 179727B0 865A8918 DA3EDBEB CF9B14CE6CBA CEDB7B7B7C7026 C1254B 3320515B8F437B9CF417B9B9B9B9B9B9B9B7CF032EA15 D1721D03 F482D7CE 6E74FEF6 D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F因为E8F3 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328 06A1D58B B7C57DA76 F50AA3D 8A1FB19CCB1 13D55C DA569EC F29632 F486E6F467B947B4E9B9F467B9B9B9C57EFFFFFFFFFFFFFF

The generator is: 2.

发电机是:2。

7. 8192-bit MODP Group
7. 8192位MODP组

This group is assigned id 18.

此组被分配了id 18。

   This prime is: 2^8192 - 2^8128 - 1 + 2^64 * { [2^8062 pi] + 4743158 }
        
   This prime is: 2^8192 - 2^8128 - 1 + 2^64 * { [2^8062 pi] + 4743158 }
        

Its hexadecimal value is:

其十六进制值为:

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

FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED EE386B5A899FA5 AE9F2411 7C4B16 49286651 45B3 6D C20078 A16305 BF4565655CFD36粪便1C62F356 208552BB 9ED52907 7096966D 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2EC3B E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D 04507A33 A521AB DF1BA64 ECFB850A 8B5F5A 8AE157 5D0607E40A 8E407E408AEC 197E407E40C 8AEC9DCEE3D226 1AD26B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C BBE1757 7A615D6C 77098C0 BAD946E208E24FA0 74E5AB31 43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBC2DB 04DE8EFC18 2EBC16 287C5947B965BFC1861F612970 CEE2D7AF B81BDD76 21704811C D0069127 D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492 36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD FF9406 AD9E530E E538DB382F 413001AE B06A553ED 9027D831 179727B0 865A8918 DA3EDBEB CF9B14CE6CBA CEDB7B7B7C7026 C1254B 3320515B8F437B9CF417B9B9B9B9B9B9B9B7CF032EA15 D1721D03 F482D7CE 6E74FEF6 D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F因为E8E8F3 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328 06A1D58B B7C57DA76 F50AA3D 8A1FB19CCB1 13D55C DA569EC F29632 F468E6F467B9B9E6B9B9B9B9B9B9B9B9B9B9B9B19715E74A3926F 12AB639C 5AE4F568 3423B474 2BF 8CB6 A932DF8B931BA 3BC832B6 8D9DD300 741FA7BF 8AFC47ED 2576F693 6BA42466 3AB639C 5AE4F568 3423B474 2BF1 C978 238F16CB E39D652D E3FDB8BE FC848AD9 2222 E04 A4037C07 13EB57A8 1A23F0C7 3473FC64 6CEAB306B 4BC886 2FAD468B7F 287F 287B737F 13CF8B336 AB287B737B364597E899 A0255DC1 64F31C5 0846851D F9AB4819 5DED7EA1 B1D510BD 7EE74D73 FAF36BC3 1ECFA268 359046F4 EB879F92 4009438B 481C6CD7 889A002E D5EE382B C9190DA6 FC026E47 5677E9E3050E2 765694DF C81F56E8 80B96E71 60C980DD 98EDDFFFFFFFFFFFFFFF

The generator is: 2.

发电机是:2。

8. Security Considerations
8. 安全考虑

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.

本文档描述了在IKE中使用的新组。这里定义的组的强度总是估计值,估计它们的方法和密码学家的方法一样多。对于下面的强度估算,我们采用了比例尺的两端,因此实际强度估算可能介于此处给出的两个数字之间。

   +--------+----------+---------------------+---------------------+
   | 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- |
   +--------+----------+---------------------+---------------------+
        
   +--------+----------+---------------------+---------------------+
   | 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
9. IANA考虑

IKE [RFC-2409] defines 4 Diffie-Hellman Groups, numbered 1 through 4.

IKE[RFC-2409]定义了4个Diffie-Hellman组,编号为1到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.

本文档定义了一个新的组5,以及从14到18的新组。通过RFC 2434[RFC-2434]中定义的“IETF共识”请求额外分配。具体而言,新的组预计将记录在标准跟踪RFC中。

10. Normative References
10. 规范性引用文件

[RFC-2409] Harkins, D. and D. Carrel, "The Internet Key Exchange (IKE)", RFC 2409, November 1998.

[RFC-2409]Harkins,D.和D.Carrel,“互联网密钥交换(IKE)”,RFC 2409,1998年11月。

[RFC-2434] Narten, T. and H. Alvestrand, "Guidelines for Writing an IANA Considerations Section in RFCs", BCP 26, RFC 2434, October 1998.

[RFC-2434]Narten,T.和H.Alvestrand,“在RFC中编写IANA注意事项部分的指南”,BCP 26,RFC 2434,1998年10月。

11. Non-Normative References
11. 非规范性引用文件
   [AES]        NIST, FIPS PUB 197, "Advanced Encryption Standard
                (AES)," November 2001.
                http://csrc.nist.gov/publications/fips/fips197/fips-
                197.{ps,pdf}
        
   [AES]        NIST, FIPS PUB 197, "Advanced Encryption Standard
                (AES)," November 2001.
                http://csrc.nist.gov/publications/fips/fips197/fips-
                197.{ps,pdf}
        

[RFC-2412] Orman, H., "The OAKLEY Key Determination Protocol", RFC 2412, November 1998.

[RFC-2412]Orman,H.,“奥克利密钥确定协议”,RFC 2412,1998年11月。

[Orman01] Orman, H. and P. Hoffman, "Determining Strengths For Public Keys Used For Exchanging Symmetric Keys", Work in progress.

[Orman01]Orman,H.和P.Hoffman,“确定用于交换对称密钥的公钥的强度”,工作正在进行中。

   [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
        
   [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
        
   [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
12. 作者地址

Tero Kivinen SSH Communications Security Corp Fredrikinkatu 42 FIN-00100 HELSINKI Finland

Tero Kivinen SSH通信安全公司Fredrikinkatu 42 FIN-00100芬兰赫尔辛基

   EMail: kivinen@ssh.fi
        
   EMail: kivinen@ssh.fi
        

Mika Kojo HELSINKI Finland

芬兰赫尔辛基米卡·科乔

   EMail: mika.kojo@helsinki.fi
        
   EMail: mika.kojo@helsinki.fi
        
13. Full Copyright Statement
13. 完整版权声明

Copyright (C) The Internet Society (2003). All Rights Reserved.

版权所有(C)互联网协会(2003年)。版权所有。

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.

本文件及其译本可复制并提供给他人,对其进行评论或解释或协助其实施的衍生作品可全部或部分编制、复制、出版和分发,不受任何限制,前提是上述版权声明和本段包含在所有此类副本和衍生作品中。但是,不得以任何方式修改本文件本身,例如删除版权通知或对互联网协会或其他互联网组织的引用,除非出于制定互联网标准的需要,在这种情况下,必须遵循互联网标准过程中定义的版权程序,或根据需要将其翻译成英语以外的其他语言。

The limited permissions granted above are perpetual and will not be revoked by the Internet Society or its successors or assigns.

上述授予的有限许可是永久性的,互联网协会或其继承人或受让人不会撤销。

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.

本文件和其中包含的信息是按“原样”提供的,互联网协会和互联网工程任务组否认所有明示或暗示的保证,包括但不限于任何保证,即使用本文中的信息不会侵犯任何权利,或对适销性或特定用途适用性的任何默示保证。

Acknowledgement

确认

Funding for the RFC Editor function is currently provided by the Internet Society.

RFC编辑功能的资金目前由互联网协会提供。