Movatterモバイル変換

Network Working Group                                          M. FriedlRequest for Comments: 4419                                     N. ProvosCategory: Standards Track                                     W. Simpson                                                              March 2006Diffie-Hellman Group Exchange forthe Secure Shell (SSH) Transport Layer ProtocolStatus 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 (2006).Abstract   This memo describes a new key exchange method for the Secure Shell   (SSH) protocol.  It allows the SSH server to propose new groups on   which to perform the Diffie-Hellman key exchange to the client.  The   proposed groups need not be fixed and can change with time.1.  Overview and Rationale   SSH [RFC4251] is a very common protocol for secure remote login on   the Internet.  Currently, SSH performs the initial key exchange using   the "diffie-hellman-group1-sha1" method [RFC4253].  This method   prescribes a fixed group on which all operations are performed.   The Diffie-Hellman key exchange provides a shared secret that cannot   be determined by either party alone.  Furthermore, the shared secret   is known only to the participant parties.  In SSH, the key exchange   is signed with the host key to provide host authentication.   The security of the Diffie-Hellman key exchange is based on the   difficulty of solving the Discrete Logarithm Problem (DLP).  Since we   expect that the SSH protocol will be in use for many years in the   future, we fear that extensive precomputation and more efficient   algorithms to compute the discrete logarithm over a fixed group might   pose a security threat to the SSH protocol.Friedl, et al.              Standards Track                     [Page 1]

RFC 4419                 SSH DH Group Exchange                March 2006   The ability to propose new groups will reduce the incentive to use   precomputation for more efficient calculation of the discrete   logarithm.  The server can constantly compute new groups in the   background.2.  Requirements Notation   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this   document are to be interpreted as described in [RFC2119].3.  Diffie-Hellman Group and Key Exchange   The server keeps a list of safe primes and corresponding generators   that it can select from.  A prime p is safe if p = 2q + 1 and q is   prime.  New primes can be generated in the background.   The generator g should be chosen such that the order of the generated   subgroup does not factor into small primes; that is, with p = 2q + 1,   the order has to be either q or p - 1.  If the order is p - 1, then   the exponents generate all possible public values, evenly distributed   throughout the range of the modulus p, without cycling through a   smaller subset.  Such a generator is called a "primitive root" (which   is trivial to find when p is "safe").   The client requests a modulus from the server indicating the   preferred size.  In the following description (C is the client, S is   the server, the modulus p is a large safe prime, and g is a generator   for a subgroup of GF(p), min is the minimal size of p in bits that is   acceptable to the client, n is the size of the modulus p in bits that   the client would like to receive from the server, max is the maximal   size of p in bits that the client can accept, V_S is S's version   string, V_C is C's version string, K_S is S's public host key, I_C is   C's KEXINIT message, and I_S is S's KEXINIT message that has been   exchanged before this part begins):   1.  C sends "min || n || max" to S, indicating the minimal acceptable       group size, the preferred size of the group, and the maximal       group size in bits the client will accept.   2.  S finds a group that best matches the client's request, and sends       "p || g" to C.   3.  C generates a random number x, where 1 < x < (p-1)/2.  It       computes e = g^x mod p, and sends "e" to S.Friedl, et al.              Standards Track                     [Page 2]

RFC 4419                 SSH DH Group Exchange                March 2006   4.  S generates a random number y, where 0 < y < (p-1)/2, and       computes f = g^y mod p.  S receives "e".  It computes K = e^y mod       p, H = hash(V_C || V_S || I_C || I_S || K_S || min || n || max ||       p || g || e || f || K) (these elements are encoded according to       their types; see below), and signature s on H with its private       host key.  S sends "K_S || f || s" to C.  The signing operation       may involve a second hashing operation.   5.  C verifies that K_S really is the host key for S (e.g., using       certificates or a local database to obtain the public key).  C is       also allowed to accept the key without verification; however,       doing so will render the protocol insecure against active attacks       (but may be desirable for practical reasons in the short term in       many environments).  C then computes K = f^x mod p, H = hash(V_C       || V_S || I_C || I_S || K_S || min || n || max || p || g || e ||       f || K), and verifies the signature s on H.   Servers and clients SHOULD support groups with a modulus length of k   bits, where 1024 <= k <= 8192.  The recommended values for min and   max are 1024 and 8192, respectively.   Either side MUST NOT send or accept e or f values that are not in the   range [1, p-1].  If this condition is violated, the key exchange   fails.  To prevent confinement attacks, they MUST accept the shared   secret K only if 1 < K < p - 1.   The server should return the smallest group it knows that is larger   than the size the client requested.  If the server does not know a   group that is larger than the client request, then it SHOULD return   the largest group it knows.  In all cases, the size of the returned   group SHOULD be at least 1024 bits.   This is implemented with the following messages.  The hash algorithm   for computing the exchange hash is defined by the method name, and is   called HASH.  The public key algorithm for signing is negotiated with   the KEXINIT messages.   First, the client sends:     byte    SSH_MSG_KEY_DH_GEX_REQUEST     uint32  min, minimal size in bits of an acceptable group     uint32  n, preferred size in bits of the group the server will send     uint32  max, maximal size in bits of an acceptable groupFriedl, et al.              Standards Track                     [Page 3]

RFC 4419                 SSH DH Group Exchange                March 2006   The server responds with     byte    SSH_MSG_KEX_DH_GEX_GROUP     mpint   p, safe prime     mpint   g, generator for subgroup in GF(p)   The client responds with:     byte    SSH_MSG_KEX_DH_GEX_INIT     mpint   e   The server responds with:     byte    SSH_MSG_KEX_DH_GEX_REPLY     string  server public host key and certificates (K_S)     mpint   f     string  signature of H   The hash H is computed as the HASH hash of the concatenation of the   following:     string  V_C, the client's version string (CR and NL excluded)     string  V_S, the server's version string (CR and NL excluded)     string  I_C, the payload of the client's SSH_MSG_KEXINIT     string  I_S, the payload of the server's SSH_MSG_KEXINIT     string  K_S, the host key     uint32  min, minimal size in bits of an acceptable group     uint32  n, preferred size in bits of the group the server will send     uint32  max, maximal size in bits of an acceptable group     mpint   p, safe prime     mpint   g, generator for subgroup     mpint   e, exchange value sent by the client     mpint   f, exchange value sent by the server     mpint   K, the shared secret   This value is called the exchange hash, and it is used to   authenticate the key exchange as per [RFC4253].4.  Key Exchange Methods   This document defines two new key exchange methods:   "diffie-hellman-group-exchange-sha1" and   "diffie-hellman-group-exchange-sha256".Friedl, et al.              Standards Track                     [Page 4]

RFC 4419                 SSH DH Group Exchange                March 20064.1.  diffie-hellman-group-exchange-sha1   The "diffie-hellman-group-exchange-sha1" method specifies   Diffie-Hellman Group and Key Exchange with SHA-1 [FIPS-180-2] as   HASH.4.2.  diffie-hellman-group-exchange-sha256   The "diffie-hellman-group-exchange-sha256" method specifies   Diffie-Hellman Group and Key Exchange with SHA-256 [FIPS-180-2] as   HASH.   Note that the hash used in key exchange (in this case, SHA-256) must   also be used in the key derivation pseudo-random function (PRF), as   per the requirement in the "Output from Key Exchange" section in   [RFC4253].5.  Summary of Message Numbers   The following message numbers have been defined in this document.   They are in a name space private to this document and not assigned by   IANA.     #define SSH_MSG_KEX_DH_GEX_REQUEST_OLD  30     #define SSH_MSG_KEX_DH_GEX_REQUEST      34     #define SSH_MSG_KEX_DH_GEX_GROUP        31     #define SSH_MSG_KEX_DH_GEX_INIT         32     #define SSH_MSG_KEX_DH_GEX_REPLY        33   SSH_MSG_KEX_DH_GEX_REQUEST_OLD is used for backward compatibility.   Instead of sending "min || n || max", the client only sends "n".  In   addition, the hash is calculated using only "n" instead of "min || n   || max".   The numbers 30-49 are key exchange specific and may be redefined by   other kex methods.6.  Implementation Notes6.1.  Choice of Generator   One useful technique is to select the generator, and then limit the   modulus selection sieve to primes with that generator:      2   when p (mod 24) = 11.      5   when p (mod 10) = 3 or 7.Friedl, et al.              Standards Track                     [Page 5]

RFC 4419                 SSH DH Group Exchange                March 2006   It is recommended to use 2 as generator, because it improves   efficiency in multiplication performance.  It is usable even when it   is not a primitive root, as it still covers half of the space of   possible residues.6.2.  Private Exponents   To increase the speed of the key exchange, both client and server may   reduce the size of their private exponents.  It should be at least   twice as long as the key material that is generated from the shared   secret.  For more details, see the paper by van Oorschot and Wiener   [VAN-OORSCHOT].7.  Security Considerations   This protocol aims to be simple and uses only well-understood   primitives.  This encourages acceptance by the community and allows   for ease of implementation, which hopefully leads to a more secure   system.   The use of multiple moduli inhibits a determined attacker from   precalculating moduli exchange values, and discourages dedication of   resources for analysis of any particular modulus.   It is important to employ only safe primes as moduli, as they allow   us to find a generator g so that the order of the generated subgroup   does not factor into small primes, that is, with p = 2q + 1, the   order has to be either q or p - 1.  If the order is p - 1, then the   exponents generate all possible public values, evenly distributed   throughout the range of the modulus p, without cycling through a   smaller subset.  Van Oorshot and Wiener note that using short private   exponents with a random prime modulus p makes the computation of the   discrete logarithm easy [VAN-OORSCHOT].  However, they also state   that this problem does not apply to safe primes.   The least significant bit of the private exponent can be recovered   when the modulus is a safe prime [MENEZES].  However, this is not a   problem if the size of the private exponent is big enough.  Related   to this, Waldvogel and Massey note: When private exponents are chosen   independently and uniformly at random from {0,...,p-2}, the key   entropy is less than 2 bits away from the maximum, lg(p-1)   [WALDVOGEL].   The security considerations in [RFC4251] also apply to this key   exchange method.Friedl, et al.              Standards Track                     [Page 6]

RFC 4419                 SSH DH Group Exchange                March 20068.  Acknowledgements   The document is derived in part from "SSH Transport Layer Protocol"   [RFC4253] by T. Ylonen, T. Kivinen, M. Saarinen, T.  Rinne, and S.   Lehtinen.   Markku-Juhani Saarinen pointed out that the least significant bit of   the private exponent can be recovered efficiently when using safe   primes and a subgroup with an order divisible by two.   Bodo Moeller suggested that the server send only one group, reducing   the complexity of the implementation and the amount of data that   needs to be exchanged between client and server.Friedl, et al.              Standards Track                     [Page 7]

RFC 4419                 SSH DH Group Exchange                March 2006Appendix A:  Generation of Safe Primes   The "Handbook of Applied Cryptography" [MENEZES] lists the following   algorithm to generate a k-bit safe prime p.  It has been modified so   that 2 is a generator for the multiplicative group mod p.   1.  Do the following:       1.  Select a random (k-1)-bit prime q, so that q mod 12 = 5.       2.  Compute p := 2q + 1, and test whether p is prime (using,           e.g., trial division and the Rabin-Miller test).   2.  Repeat until p is prime.   If an implementation uses the OpenSSL libraries, a group consisting   of a 1024-bit safe prime and 2 as generator can be created as   follows:       DH *d = NULL;       d = DH_generate_parameters(1024, DH_GENERATOR_2, NULL, NULL);       BN_print_fp(stdout, d->p);   The order of the subgroup generated by 2 is q = p - 1.ReferencesNormative References   [FIPS-180-2]   National Institute of Standards and Technology (NIST),                  "Secure Hash Standard (SHS)", FIPS PUB 180-2,                  August 2002.   [RFC4251]      Ylonen, T. and C. Lonvick, "The Secure Shell (SSH)                  Protocol Architecture",RFC 4251, January 2006.   [RFC4253]      Lonvick, C., "The Secure Shell (SSH) Transport Layer                  Protocol",RFC 4253, January 2006.   [RFC2119]      Bradner, S., "Key words for use in RFCs to Indicate                  Requirement Levels",BCP 14,RFC 2119, March 1997.Informative References   [MENEZES]      Menezes, A., van Oorschot, P., and S. Vanstone,                  "Handbook of Applied Cryptography", CRC Press, p. 537,                  1996.Friedl, et al.              Standards Track                     [Page 8]

RFC 4419                 SSH DH Group Exchange                March 2006   [VAN-OORSCHOT] van Oorschot, P. and M. Wiener, "On Diffie-Hellman key                  agreement with short exponents", Advances in                  Cryptology -EUROCRYPT'96, LNCS 1070,                  Springer-Verlag, pp. 332-343, 1996.   [WALDVOGEL]    Waldvogel, C. and J. Massey, "The probability                  distribution of the Diffie-Hellman key", Proceedings                  of AUSCRYPT 92, LNCS 718, Springer-Verlag, pp.                  492-504, 1993.Authors' Addresses   Markus Friedl   EMail: markus@openbsd.org   Niels Provos   EMail: provos@citi.umich.edu   William A. Simpson   EMail: wsimpson@greendragon.comFriedl, et al.              Standards Track                     [Page 9]

RFC 4419                 SSH DH Group Exchange                March 2006Full Copyright Statement   Copyright (C) The Internet Society (2006).   This document is subject to the rights, licenses and restrictions   contained inBCP 78, and except as set forth therein, the authors   retain all their rights.   This document and the information contained herein are provided on an   "AS IS" basis and THE CONTRIBUTOR, THE ORGANIZATION HE/SHE REPRESENTS   OR IS SPONSORED BY (IF ANY), THE INTERNET SOCIETY AND THE INTERNET   ENGINEERING TASK FORCE DISCLAIM 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.Intellectual Property   The IETF takes no position regarding the validity or scope of any   Intellectual Property Rights or other rights that might be claimed to   pertain to the implementation or use of the technology described in   this document or the extent to which any license under such rights   might or might not be available; nor does it represent that it has   made any independent effort to identify any such rights.  Information   on the procedures with respect to rights in RFC documents can be   found inBCP 78 andBCP 79.   Copies of IPR disclosures made to the IETF Secretariat and any   assurances of licenses to be made available, or the result of an   attempt made to obtain a general license or permission for the use of   such proprietary rights by implementers or users of this   specification can be obtained from the IETF on-line IPR repository athttp://www.ietf.org/ipr.   The IETF invites any interested party to bring to its attention any   copyrights, patents or patent applications, or other proprietary   rights that may cover technology that may be required to implement   this standard.  Please address the information to the IETF at   ietf-ipr@ietf.org.Acknowledgement   Funding for the RFC Editor function is provided by the IETF   Administrative Support Activity (IASA).Friedl, et al.              Standards Track                    [Page 10]