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rfc:rfc5656

Network Working Group D. Stebila Request for Comments: 5656 Queensland University of Technology Category: Standards Track J. Green

                                                    Queen's University
                                                         December 2009

Elliptic Curve Algorithm Integration in the Secure Shell Transport Layer

Abstract

 This document describes algorithms based on Elliptic Curve
 Cryptography (ECC) for use within the Secure Shell (SSH) transport
 protocol.  In particular, it specifies Elliptic Curve Diffie-Hellman
 (ECDH) key agreement, Elliptic Curve Menezes-Qu-Vanstone (ECMQV) key
 agreement, and Elliptic Curve Digital Signature Algorithm (ECDSA) for
 use in the SSH Transport Layer protocol.

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) 2009 IETF Trust and the persons identified as the
 document authors.  All rights reserved.
 This document is subject to BCP 78 and the IETF Trust's Legal
 Provisions Relating to IETF Documents
 (http://trustee.ietf.org/license-info) in effect on the date of
 publication of this document.  Please review these documents
 carefully, as they describe your rights and restrictions with respect
 to this document.  Code Components extracted from this document must
 include Simplified BSD License text as described in Section 4.e of
 the Trust Legal Provisions and are provided without warranty as
 described in the BSD License.
 This document may contain material from IETF Documents or IETF
 Contributions published or made publicly available before November
 10, 2008.  The person(s) controlling the copyright in some of this
 material may not have granted the IETF Trust the right to allow
 modifications of such material outside the IETF Standards Process.
 Without obtaining an adequate license from the person(s) controlling
 the copyright in such materials, this document may not be modified

Stebila & Green Standards Track [Page 1] RFC 5656 SSH ECC Algorithm Integration December 2009

 outside the IETF Standards Process, and derivative works of it may
 not be created outside the IETF Standards Process, except to format
 it for publication as an RFC or to translate it into languages other
 than English.

Table of Contents

 1. Introduction ....................................................3
 2. Notation ........................................................4
 3. SSH ECC Public Key Algorithm ....................................4
    3.1. Key Format .................................................4
         3.1.1. Signature Algorithm .................................5
         3.1.2. Signature Encoding ..................................5
 4. ECDH Key Exchange ...............................................5
 5. ECMQV Key Exchange ..............................................8
 6. Method Names ...................................................10
    6.1. Elliptic Curve Domain Parameter Identifiers ...............10
    6.2. ECC Public Key Algorithm (ecdsa-sha2-*) ...................11
         6.2.1. Elliptic Curve Digital Signature Algorithm .........11
    6.3. ECDH Key Exchange Method Names (ecdh-sha2-*) ..............12
    6.4. ECMQV Key Exchange and Verification Method Name
         (ecmqv-sha2) ..............................................12
 7. Key Exchange Messages ..........................................13
    7.1. ECDH Message Numbers ......................................13
    7.2. ECMQV Message Numbers .....................................13
 8. Manageability Considerations ...................................13
    8.1. Control of Function through Configuration and Policy ......13
    8.2. Impact on Network Operation ...............................14
 9. Security Considerations ........................................14
 10. Named Elliptic Curve Domain Parameters ........................16
    10.1. Required Curves ..........................................16
    10.2. Recommended Curves .......................................17
 11. IANA Considerations ...........................................17
 12. References ....................................................18
    12.1. Normative References .....................................18
    12.2. Informative References ...................................19
 Appendix A.  Acknowledgements .....................................20

Stebila & Green Standards Track [Page 2] RFC 5656 SSH ECC Algorithm Integration December 2009

1. Introduction

 This document adds the following elliptic curve cryptography
 algorithms to the Secure Shell arsenal: Elliptic Curve Diffie-Hellman
 (ECDH) and Elliptic Curve Digital Signature Algorithm (ECDSA), as
 well as utilizing the SHA2 family of secure hash algorithms.
 Additionally, support is provided for Elliptic Curve Menezes-Qu-
 Vanstone (ECMQV).
 Due to its small key sizes and its inclusion in the National Security
 Agency's Suite B, Elliptic Curve Cryptography (ECC) is becoming a
 widely utilized and attractive public-key cryptosystem.
 Compared to cryptosystems such as RSA, the Digital Signature
 Algorithm (DSA), and Diffie-Hellman (DH) key exchange, ECC variations
 on these schemes offer equivalent security with smaller key sizes.
 This is illustrated in the following table, based on Section 5.6.1 of
 NIST 800-57 [NIST-800-57], which gives approximate comparable key
 sizes for symmetric- and asymmetric-key cryptosystems based on the
 best known algorithms for attacking them.  L is the field size and N
 is the sub-field size.
    +-----------+------------------------------+-------+---------+
    | Symmetric | Discrete Log (e.g., DSA, DH) |  RSA  |   ECC   |
    +-----------+------------------------------+-------+---------+
    |     80    |       L = 1024, N = 160      |  1024 | 160-223 |
    |           |                              |       |         |
    |    112    |       L = 2048, N = 256      |  2048 | 224-255 |
    |           |                              |       |         |
    |    128    |       L = 3072, N = 256      |  3072 | 256-383 |
    |           |                              |       |         |
    |    192    |       L = 7680, N = 384      |  7680 | 384-511 |
    |           |                              |       |         |
    |    256    |      L = 15360, N = 512      | 15360 |   512+  |
    +-----------+------------------------------+-------+---------+
 Implementation of this specification requires familiarity with both
 SSH [RFC4251] [RFC4253] [RFC4250] and ECC [SEC1] (additional
 information on ECC available in [HMV04], [ANSI-X9.62], and
 [ANSI-X9.63]).
 This document is concerned with SSH implementation details;
 specification of the underlying cryptographic algorithms is left to
 other standards documents.

Stebila & Green Standards Track [Page 3] RFC 5656 SSH ECC Algorithm Integration December 2009

2. 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].
 The data types boolean, byte, uint32, uint64, string, and mpint are
 to be interpreted in this document as described in [RFC4251].
 The size of a set of elliptic curve domain parameters on a prime
 curve is defined as the number of bits in the binary representation
 of the field order, commonly denoted by p.  Size on a
 characteristic-2 curve is defined as the number of bits in the binary
 representation of the field, commonly denoted by m.  A set of
 elliptic curve domain parameters defines a group of order n generated
 by a base point P.

3. SSH ECC Public Key Algorithm

 The SSH ECC public key algorithm is defined by its key format,
 corresponding signature algorithm ECDSA, signature encoding, and
 algorithm identifiers.
 This section defines the family of "ecdsa-sha2-*" public key formats
 and corresponding signature formats.  Every compliant SSH ECC
 implementation MUST implement this public key format.

3.1. Key Format

 The "ecdsa-sha2-*" key formats all have the following encoding:
    string   "ecdsa-sha2-[identifier]"
    byte[n]  ecc_key_blob
 The ecc_key_blob value has the following specific encoding:
    string   [identifier]
    string   Q
 The string [identifier] is the identifier of the elliptic curve
 domain parameters.  The format of this string is specified in
 Section 6.1.  Information on the REQUIRED and RECOMMENDED sets of
 elliptic curve domain parameters for use with this algorithm can be
 found in Section 10.
 Q is the public key encoded from an elliptic curve point into an
 octet string as defined in Section 2.3.3 of [SEC1]; point compression
 MAY be used.

Stebila & Green Standards Track [Page 4] RFC 5656 SSH ECC Algorithm Integration December 2009

 The algorithm for ECC key generation can be found in Section 3.2 of
 [SEC1].  Given some elliptic curve domain parameters, an ECC key pair
 can be generated containing a private key (an integer d), and a
 public key (an elliptic curve point Q).

3.1.1. Signature Algorithm

 Signing and verifying is done using the Elliptic Curve Digital
 Signature Algorithm (ECDSA).  ECDSA is specified in [SEC1].  The
 message hashing algorithm MUST be from the SHA2 family of hash
 functions [FIPS-180-3] and is chosen according to the curve size as
 specified in Section 6.2.1.

3.1.2. Signature Encoding

 Signatures are encoded as follows:
    string   "ecdsa-sha2-[identifier]"
    string   ecdsa_signature_blob
 The string [identifier] is the identifier of the elliptic curve
 domain parameters.  The format of this string is specified in
 Section 6.1.  Information on the REQUIRED and RECOMMENDED sets of
 elliptic curve domain parameters for use with this algorithm can be
 found in Section 10.
 The ecdsa_signature_blob value has the following specific encoding:
    mpint    r
    mpint    s
 The integers r and s are the output of the ECDSA algorithm.
 The width of the integer fields is determined by the curve being
 used.  Note that the integers r and s are integers modulo the order
 of the cryptographic subgroup, which may be larger than the size of
 the finite field.

4. ECDH Key Exchange

 The Elliptic Curve Diffie-Hellman (ECDH) key exchange method
 generates a shared secret from an ephemeral local elliptic curve
 private key and ephemeral remote elliptic curve public key.  This key
 exchange method provides explicit server authentication as defined in
 [RFC4253] using a signature on the exchange hash.  Every compliant
 SSH ECC implementation MUST implement ECDH key exchange.

Stebila & Green Standards Track [Page 5] RFC 5656 SSH ECC Algorithm Integration December 2009

 The primitive used for shared key generation is ECDH with cofactor
 multiplication, the full specification of which can be found in
 Section 3.3.2 of [SEC1].  The algorithm for key pair generation can
 be found in Section 3.2.1 of [SEC1].
 The family of key exchange method names defined for use with this key
 exchange can be found in Section 6.3.  Algorithm negotiation chooses
 the public key algorithm to be used for signing and the method name
 of the key exchange.  The method name of the key exchange chosen
 determines the elliptic curve domain parameters and hash function to
 be used in the remainder of this section.
 Information on the REQUIRED and RECOMMENDED elliptic curve domain
 parameters for use with this method can be found in Section 10.
 All elliptic curve public keys MUST be validated after they are
 received.  An example of a validation algorithm can be found in
 Section 3.2.2 of [SEC1].  If a key fails validation, the key exchange
 MUST fail.
 The elliptic curve public keys (points) that must be transmitted are
 encoded into octet strings before they are transmitted.  The
 transformation between elliptic curve points and octet strings is
 specified in Sections 2.3.3 and 2.3.4 of [SEC1]; point compression
 MAY be used.  The output of shared key generation is a field element
 xp.  The SSH framework requires that the shared key be an integer.
 The conversion between a field element and an integer is specified in
 Section 2.3.9 of [SEC1].
 Specification of the message numbers SSH_MSG_KEX_ECDH_INIT and
 SSH_MSG_KEX_ECDH_REPLY is found in Section 7.

Stebila & Green Standards Track [Page 6] RFC 5656 SSH ECC Algorithm Integration December 2009

 The following is an overview of the key exchange process:
    Client                                                Server
    ------                                                ------
    Generate ephemeral key pair.
    SSH_MSG_KEX_ECDH_INIT  -------------->
                                    Verify received key is valid.
                                     Generate ephemeral key pair.
                                           Compute shared secret.
                                 Generate and sign exchange hash.
                           <------------- SSH_MSG_KEX_ECDH_REPLY
    Verify received key is valid.
    *Verify host key belongs to server.
    Compute shared secret.
    Generate exchange hash.
    Verify server's signature.
  • It is RECOMMENDED that the client verify that the host key sent

is the server's host key (for example, using a local database).

       The client MAY accept the host key without verification, but
       doing so will render the protocol insecure against active
       attacks; see the discussion in Section 4.1 of [RFC4251].
 This is implemented using the following messages.
 The client sends:
    byte     SSH_MSG_KEX_ECDH_INIT
    string   Q_C, client's ephemeral public key octet string
 The server responds with:
    byte     SSH_MSG_KEX_ECDH_REPLY
    string   K_S, server's public host key
    string   Q_S, server's ephemeral public key octet string
    string   the signature on the exchange hash

Stebila & Green Standards Track [Page 7] RFC 5656 SSH ECC Algorithm Integration December 2009

 The exchange hash H is computed as the hash of the concatenation of
 the following.
    string   V_C, client's identification string (CR and LF excluded)
    string   V_S, server's identification string (CR and LF excluded)
    string   I_C, payload of the client's SSH_MSG_KEXINIT
    string   I_S, payload of the server's SSH_MSG_KEXINIT
    string   K_S, server's public host key
    string   Q_C, client's ephemeral public key octet string
    string   Q_S, server's ephemeral public key octet string
    mpint    K,   shared secret

5. ECMQV Key Exchange

 The Elliptic Curve Menezes-Qu-Vanstone (ECMQV) key exchange algorithm
 generates a shared secret from two local elliptic curve key pairs and
 two remote public keys.  This key exchange method provides implicit
 server authentication as defined in [RFC4253].  The ECMQV key
 exchange method is OPTIONAL.
 The key exchange method name defined for use with this key exchange
 is "ecmqv-sha2".  This method name gives a hashing algorithm that is
 to be used for the Hashed Message Authentication Code (HMAC) below.
 Future RFCs may define new method names specifying new hash
 algorithms for use with ECMQV.  More information about the method
 name and HMAC can be found in Section 6.4.
 In general, the ECMQV key exchange is performed using the ephemeral
 and long-term key pair of both the client and server, which is a
 total of 4 keys.  Within the framework of SSH, the client does not
 have a long-term key pair that needs to be authenticated.  Therefore,
 we generate an ephemeral key and use that as both the clients keys.
 This is more efficient than using two different ephemeral keys, and
 it does not adversely affect security (it is analogous to the one-
 pass protocol in Section 6.1 of [LMQSV98]).
 A full description of the ECMQV primitive can be found in Section 3.4
 of [SEC1].  The algorithm for key pair generation can be found in
 Section 3.2.1 of [SEC1].
 During algorithm negotiation with the SSH_MSG_KEXINIT messages, the
 ECMQV key exchange method can only be chosen if a public key
 algorithm supporting ECC host keys can also be chosen.  This is due
 to the use of implicit server authentication in this key exchange
 method.  This case is handled the same way that key exchange methods
 requiring encryption/signature capable public key algorithms are

Stebila & Green Standards Track [Page 8] RFC 5656 SSH ECC Algorithm Integration December 2009

 handled in Section 7.1 of [RFC4253].  If ECMQV key exchange is
 chosen, then the public key algorithm supporting ECC host keys MUST
 also be chosen.
 ECMQV requires that all the keys used to generate a shared secret are
 generated over the same elliptic curve domain parameters.  Since the
 host key is used in the generation of the shared secret, allowing for
 implicit server authentication, the domain parameters associated with
 the host key are used throughout this section.
 All elliptic curve public keys MUST be validated after they are
 received.  An example of a validation algorithm can be found in
 Section 3.2.2 of [SEC1].  If a key fails validation, the key exchange
 MUST fail.
 The elliptic curve ephemeral public keys (points) that must be
 transmitted are encoded into octet strings before they are
 transmitted.  The transformation between elliptic curve points and
 octet strings is specified in Sections 2.3.3 and 2.3.4 of [SEC1];
 point compression MAY be used.  The output of shared key generation
 is a field element xp.  The SSH framework requires that the shared
 key be an integer.  The conversion between a field element and an
 integer is specified in Section 2.3.9 of [SEC1].
 The following is an overview of the key exchange process:
    Client                                                Server
    ------                                                ------
    Generate ephemeral key pair.
    SSH_MSG_KEX_ECMQV_INIT ------------->
                                    Verify received key is valid.
                                     Generate ephemeral key pair.
                                           Compute shared secret.
                              Generate exchange hash and compute
                            HMAC over it using the shared secret.
                          <------------- SSH_MSG_KEX_ECMQV_REPLY
    Verify received keys are valid.
    *Verify host key belongs to server.
    Compute shared secret.
    Verify HMAC.
  • It is RECOMMENDED that the client verify that the host key sent

is the server's host key (for example, using a local database).

       The client MAY accept the host key without verification, but
       doing so will render the protocol insecure against active
       attacks.

Stebila & Green Standards Track [Page 9] RFC 5656 SSH ECC Algorithm Integration December 2009

 The specification of the message numbers SSH_MSG_ECMQV_INIT and
 SSH_MSG_ECMQV_REPLY can be found in Section 7.
 This key exchange algorithm is implemented with the following
 messages.
 The client sends:
    byte     SSH_MSG_ECMQV_INIT
    string   Q_C, client's ephemeral public key octet string
 The server sends:
    byte     SSH_MSG_ECMQV_REPLY
    string   K_S, server's public host key
    string   Q_S, server's ephemeral public key octet string
    string   HMAC tag computed on H using the shared secret
 The hash H is formed by applying the algorithm HASH on a
 concatenation of the following:
    string   V_C, client's identification string (CR and LF excluded)
    string   V_S, server's identification string (CR and LF excluded)
    string   I_C, payload of the client's SSH_MSG_KEXINIT
    string   I_S, payload of the server's SSH_MSG_KEXINIT
    string   K_S, server's public host key
    string   Q_C, client's ephemeral public key octet string
    string   Q_S, server's ephemeral public key octet string
    mpint    K,   shared secret

6. Method Names

 This document defines a new family of key exchange method names, a
 new key exchange method name, and a new family of public key
 algorithm names in the SSH name registry.

6.1. Elliptic Curve Domain Parameter Identifiers

 This section specifies identifiers encoding named elliptic curve
 domain parameters.  These identifiers are used in this document to
 identify the curve used in the SSH ECC public key format, the ECDSA
 signature blob, and the ECDH method name.
 For the REQUIRED elliptic curves nistp256, nistp384, and nistp521,
 the elliptic curve domain parameter identifiers are the strings
 "nistp256", "nistp384", and "nistp521".

Stebila & Green Standards Track [Page 10] RFC 5656 SSH ECC Algorithm Integration December 2009

 For all other elliptic curves, including all other NIST curves and
 all other RECOMMENDED curves, the elliptic curve domain parameter
 identifier is the ASCII period-separated decimal representation of
 the Abstract Syntax Notation One (ASN.1) [ASN1] Object Identifier
 (OID) of the named curve domain parameters that are associated with
 the server's ECC host keys.  This identifier is defined provided that
 the concatenation of the public key format identifier and the
 elliptic curve domain parameter identifier (or the method name and
 the elliptic curve domain parameter identifier) does not exceed the
 maximum specified by the SSH protocol architecture [RFC4251], namely
 64 characters; otherwise, the identifier for that curve is undefined,
 and the curve is not supported by this specification.
 A list of the REQUIRED and RECOMMENDED curves and their OIDs can be
 found in Section 10.
 Note that implementations MUST use the string identifiers for the
 three REQUIRED NIST curves, even when an OID exists for that curve.

6.2. ECC Public Key Algorithm (ecdsa-sha2-*)

 The SSH ECC public key algorithm is specified by a family of public
 key format identifiers.  Each identifier is the concatenation of the
 string "ecdsa-sha2-" with the elliptic curve domain parameter
 identifier as defined in Section 6.1.  A list of the required and
 recommended curves and their OIDs can be found in Section 10.
 For example, the method name for ECDH key exchange with ephemeral
 keys generated on the nistp256 curve is "ecdsa-sha2-nistp256".

6.2.1. Elliptic Curve Digital Signature Algorithm

 The Elliptic Curve Digital Signature Algorithm (ECDSA) is specified
 for use with the SSH ECC public key algorithm.
 The hashing algorithm defined by this family of method names is the
 SHA2 family of hashing algorithms [FIPS-180-3].  The algorithm from
 the SHA2 family that will be used is chosen based on the size of the
 named curve specified in the public key:

Stebila & Green Standards Track [Page 11] RFC 5656 SSH ECC Algorithm Integration December 2009

                  +----------------+----------------+
                  |   Curve Size   | Hash Algorithm |
                  +----------------+----------------+
                  |    b <= 256    |     SHA-256    |
                  |                |                |
                  | 256 < b <= 384 |     SHA-384    |
                  |                |                |
                  |     384 < b    |     SHA-512    |
                  +----------------+----------------+

6.3. ECDH Key Exchange Method Names (ecdh-sha2-*)

 The Elliptic Curve Diffie-Hellman (ECDH) key exchange is defined by a
 family of method names.  Each method name is the concatenation of the
 string "ecdh-sha2-" with the elliptic curve domain parameter
 identifier as defined in Section 6.1.  A list of the required and
 recommended curves and their OIDs can be found in Section 10.
 For example, the method name for ECDH key exchange with ephemeral
 keys generated on the sect409k1 curve is "ecdh-sha2-1.3.132.0.36".
 The hashing algorithm defined by this family of method names is the
 SHA2 family of hashing algorithms [FIPS-180-3].  The hashing
 algorithm is defined in the method name to allow room for other
 algorithms to be defined in future documents.  The algorithm from the
 SHA2 family that will be used is chosen based on the size of the
 named curve specified in the method name according to the table in
 Section 6.2.1.
 The concatenation of any so encoded ASN.1 OID specifying a set of
 elliptic curve domain parameters with "ecdh-sha2-" is implicitly
 registered under this specification.

6.4. ECMQV Key Exchange and Verification Method Name (ecmqv-sha2)

 The Elliptic Curve Menezes-Qu-Vanstone (ECMQV) key exchange is
 defined by the method name "ecmqv-sha2".  Unlike the ECDH key
 exchange method, ECMQV relies on a public key algorithm that uses ECC
 keys: it does not need a family of method names because the curve
 information can be gained from the public key algorithm.
 The hashing and message authentication code algorithms are defined by
 the method name to allow room for other algorithms to be defined for
 use with ECMQV in future documents.

Stebila & Green Standards Track [Page 12] RFC 5656 SSH ECC Algorithm Integration December 2009

 The hashing algorithm defined by this method name is the SHA2 family
 of hashing algorithms [FIPS-180-3].  The algorithm from the SHA2
 family that will be used is chosen based on the size of the named
 curve specified for use with ECMQV by the chosen public key algorithm
 according to the table in Section 6.2.1.
 The keyed-hash message authentication code that is used to identify
 the server and verify communications is based on the hash chosen
 above.  The information on implementing the HMAC based on the chosen
 hash algorithm can be found in [RFC2104].

7. Key Exchange Messages

 The message numbers 30-49 are key-exchange-specific and in a private
 namespace defined in [RFC4250] that may be redefined by any key
 exchange method [RFC4253] without requiring an IANA registration
 process.
 The following message numbers have been defined in this document:

7.1. ECDH Message Numbers

    #define SSH_MSG_KEX_ECDH_INIT                30
    #define SSH_MSG_KEX_ECDH_REPLY               31

7.2. ECMQV Message Numbers

    #define SSH_MSG_ECMQV_INIT                   30
    #define SSH_MSG_ECMQV_REPLY                  31

8. Manageability Considerations

 As this document only provides new public key algorithms and key
 exchange methods within the existing Secure Shell protocol
 architecture, there are few manageability considerations beyond those
 that apply for existing Secure Shell implementations.  Additional
 manageability considerations are listed below.

8.1. Control of Function through Configuration and Policy

 Section 10 specifies REQUIRED and RECOMMENDED elliptic curve domain
 parameters to be used with the public key algorithms and key exchange
 methods defined in this document.  Implementers SHOULD allow system
 administrators to disable some curves, including REQUIRED or
 RECOMMENDED curves, to meet local security policy.

Stebila & Green Standards Track [Page 13] RFC 5656 SSH ECC Algorithm Integration December 2009

8.2. Impact on Network Operation

 As this document provides new functionality within the Secure Shell
 protocol architecture, the only impact on network operations is the
 impact on existing Secure Shell implementations.  The Secure Shell
 protocol provides negotiation mechanisms for public key algorithms
 and key exchange methods: any implementations that do not recognize
 the algorithms and methods defined in this document will ignore them
 in the negotiation and use the next mutually supported algorithm or
 method, causing no negative impact on backward compatibility.
 The use of elliptic curve cryptography should not place a significant
 computational burden on an implementing server.  In fact, due to its
 smaller key sizes, elliptic curve cryptography can be implemented
 more efficiently for the same security level than RSA, finite field
 Diffie-Hellman, or DSA.

9. Security Considerations

 This document provides new public key algorithms and new key
 agreement methods for the Secure Shell protocol.  For the most part,
 the security considerations involved in using the Secure Shell
 protocol apply.  Additionally, implementers should be aware of
 security considerations specific to elliptic curve cryptography.
 For all three classes of functionality added by this document (the
 public key algorithms involving ECDSA, key exchange involving ECDH,
 and authenticated key exchange involving ECMQV), the current best
 known technique for breaking the cryptosystems is by solving the
 elliptic curve discrete logarithm problem (ECDLP).
 The difficulty of breaking the ECDLP depends on the size and quality
 of the elliptic curve parameters.  Certain types of curves can be
 more susceptible to known attacks than others.  For example, curves
 over finite fields GF(2^m), where m is composite, may be susceptible
 to an attack based on the Weil descent.  All of the RECOMMENDED
 curves in Section 10 do not have this problem.  System administrators
 should be cautious when enabling curves other than the ones specified
 in Section 10 and should make a more detailed investigation into the
 security of the curve in question.
 It is believed (see, for example, Section B.2.1 of [SEC1]) that when
 curve parameters are generated at random, the curves will be
 resistant to special attacks, and must rely on the most general
 attacks.  The REQUIRED curves in Section 10 were all generated
 verifiably pseudorandomly.  The runtime of general attacks depends on
 the algorithm used.  At present, the best known algorithm is the
 Pollard-rho method.  (Shor's algorithm for quantum computers can

Stebila & Green Standards Track [Page 14] RFC 5656 SSH ECC Algorithm Integration December 2009

 solve the ECDLP in polynomial time, but at present large-scale
 quantum computers have not been constructed and significant
 experimental physics and engineering work needs to be done before
 large-scale quantum computers can be constructed.  There is no solid
 estimate as to when this may occur, but it is widely believed to be
 at least 20 years from the present.)
 Based on projections of computation power, it is possible to estimate
 the running time of the best known attacks based on the size of the
 finite field.  The table in Section 1 gives an estimate of the
 equivalence between elliptic curve field size and symmetric key size.
 Roughly speaking, an N-bit elliptic curve offers the same security as
 an N/2-bit symmetric cipher, so a 256-bit elliptic curve (such as the
 REQUIRED nistp256 curve) is suitable for use with 128-bit AES, for
 example.
 Many estimates consider that 2^80-2^90 operations are beyond
 feasible, so that would suggest using elliptic curves of at least
 160-180 bits.  The REQUIRED curves in this document are 256-, 384-,
 and 521-bit curves; implementations SHOULD NOT use curves smaller
 than 160 bits.
 A detailed discussion on the security considerations of elliptic
 curve domain parameters and the ECDH, ECDSA, and ECMQV algorithms can
 be found in Appendix B of [SEC1].
 Additionally, the key exchange methods defined in this document rely
 on the SHA2 family of hash functions, defined in [FIPS-180-3].  The
 appropriate security considerations of that document apply.  Although
 some weaknesses have been discovered in the predecessor, SHA-1, no
 weaknesses in the SHA2 family are known at present.  The SHA2 family
 consists of four variants -- SHA-224, SHA-256, SHA-384, and SHA-521
 -- named after their digest lengths.  In the absence of special
 purpose attacks exploiting the specific structure of the hash
 function, the difficulty of finding collisions, preimages, and second
 preimages for the hash function is related to the digest length.
 This document specifies in Section 6.2.1 which SHA2 variant should be
 used with which elliptic curve size based on this guidance.
 Since ECDH and ECMQV allow for elliptic curves of arbitrary sizes and
 thus arbitrary security strength, it is important that the size of
 elliptic curve be chosen to match the security strength of other
 elements of the SSH handshake.  In particular, host key sizes,
 hashing algorithms and bulk encryption algorithms must be chosen
 appropriately.  Information regarding estimated equivalence of key
 sizes is available in [NIST-800-57]; the discussion in [RFC3766] is
 also relevant.  We note in particular that when ECDSA is used as the

Stebila & Green Standards Track [Page 15] RFC 5656 SSH ECC Algorithm Integration December 2009

 signature algorithm and ECDH is used as the key exchange method, if
 curves of different sizes are used, then it is possible that
 different hash functions from the SHA2 family could be used.
 The REQUIRED and RECOMMENDED curves in this document are at present
 believed to offer security at the levels indicated in this section
 and as specified with the table in Section 1.
 System administrators and implementers should take careful
 consideration of the security issues when enabling curves other than
 the REQUIRED or RECOMMENDED curves in this document.  Not all
 elliptic curves are secure, even if they are over a large field.
 Implementers SHOULD ensure that any ephemeral private keys or random
 values -- including the value k used in ECDSA signature generation
 and the ephemeral private key values in ECDH and ECMQV -- are
 generated from a random number generator or a properly seeded
 pseudorandom number generator, are protected from leakage, are not
 reused outside of the context of the protocol in this document, and
 are erased from memory when no longer needed.

10. Named Elliptic Curve Domain Parameters

 Implementations MAY support any ASN.1 object identifier (OID) in the
 ASN.1 object tree that defines a set of elliptic curve domain
 parameters [ASN1].

10.1. Required Curves

 Every SSH ECC implementation MUST support the named curves below.
 These curves are defined in [SEC2]; the NIST curves were originally
 defined in [NIST-CURVES].  These curves SHOULD always be enabled
 unless specifically disabled by local security policy.
            +----------+-----------+---------------------+
            |   NIST*  |    SEC    |         OID         |
            +----------+-----------+---------------------+
            | nistp256 | secp256r1 | 1.2.840.10045.3.1.7 |
            |          |           |                     |
            | nistp384 | secp384r1 |     1.3.132.0.34    |
            |          |           |                     |
            | nistp521 | secp521r1 |     1.3.132.0.35    |
            +----------+-----------+---------------------+
  • For these three REQUIRED curves, the elliptic curve domain

parameter identifier is the string in the first column of the

       table, the NIST name of the curve.  (See Section 6.1.)

Stebila & Green Standards Track [Page 16] RFC 5656 SSH ECC Algorithm Integration December 2009

10.2. Recommended Curves

 It is RECOMMENDED that SSH ECC implementations also support the
 following curves.  These curves are defined in [SEC2].
            +----------+-----------+---------------------+
            |   NIST   |    SEC    |         OID*        |
            +----------+-----------+---------------------+
            | nistk163 | sect163k1 |     1.3.132.0.1     |
            |          |           |                     |
            | nistp192 | secp192r1 | 1.2.840.10045.3.1.1 |
            |          |           |                     |
            | nistp224 | secp224r1 |     1.3.132.0.33    |
            |          |           |                     |
            | nistk233 | sect233k1 |     1.3.132.0.26    |
            |          |           |                     |
            | nistb233 | sect233r1 |     1.3.132.0.27    |
            |          |           |                     |
            | nistk283 | sect283k1 |     1.3.132.0.16    |
            |          |           |                     |
            | nistk409 | sect409k1 |     1.3.132.0.36    |
            |          |           |                     |
            | nistb409 | sect409r1 |     1.3.132.0.37    |
            |          |           |                     |
            | nistt571 | sect571k1 |     1.3.132.0.38    |
            +----------+-----------+---------------------+
  • For these RECOMMENDED curves, the elliptic curve domain

parameter identifier is the string in the third column of the

       table, the ASCII representation of the OID of the curve.  (See
       Section 6.1.)

11. IANA Considerations

 Consistent with Section 8 of [RFC4251] and Section 4.6 of [RFC4250],
 this document makes the following registrations:
 In the Public Key Algorithm Names registry: The family of SSH public
 key algorithm names beginning with "ecdsa-sha2-" and not containing
 the at-sign ('@'), to name the public key algorithms defined in
 Section 3.
 In the Key Exchange Method Names registry: The family of SSH key
 exchange method names beginning with "ecdh-sha2-" and not containing
 the at-sign ('@'), to name the key exchange methods defined in
 Section 4.

Stebila & Green Standards Track [Page 17] RFC 5656 SSH ECC Algorithm Integration December 2009

 In the Key Exchange Method Names registry: The SSH key exchange
 method name "ecmqv-sha2" to name the key exchange method defined in
 Section 5.
 This document creates no new registries.

12. References

12.1. Normative References

 [ASN1]         International Telecommunications Union, "Abstract
                Syntax Notation One (ASN.1): Specification of basic
                notation",  X.680, July 2002.
 [FIPS-180-3]   National Institute of Standards and Technology,
                "Secure Hash Standard", FIPS 180-3, October 2008.
 [RFC2104]      Krawczyk, H., Bellare, M., and R. Canetti, "HMAC:
                Keyed-Hashing for Message Authentication", RFC 2104,
                February 1997.
 [RFC2119]      Bradner, S., "Key words for use in RFCs to Indicate
                Requirement Levels", BCP 14, RFC 2119, March 1997.
 [RFC3766]      Orman, H. and P. Hoffman, "Determining Strengths For
                Public Keys Used For Exchanging Symmetric Keys",
                BCP 86, RFC 3766, April 2004.
 [RFC4250]      Lehtinen, S. and C. Lonvick, "The Secure Shell (SSH)
                Protocol Assigned Numbers", RFC 4250, January 2006.
 [RFC4251]      Ylonen, T. and C. Lonvick, "The Secure Shell (SSH)
                Protocol Architecture", RFC 4251, January 2006.
 [RFC4253]      Ylonen, T. and C. Lonvick, "The Secure Shell (SSH)
                Transport Layer Protocol", RFC 4253, January 2006.
 [SEC1]         Standards for Efficient Cryptography Group, "Elliptic
                Curve Cryptography", SEC 1, May 2009,
                <http://www.secg.org/download/aid-780/sec1-v2.pdf>.
 [SEC2]         Standards for Efficient Cryptography Group,
                "Recommended Elliptic Curve Domain Parameters", SEC 2,
                September 2000,
                <http://www.secg.org/download/aid-386/sec2_final.pdf>.

Stebila & Green Standards Track [Page 18] RFC 5656 SSH ECC Algorithm Integration December 2009

12.2. Informative References

 [ANSI-X9.62]   American National Standards Institute, "Public Key
                Cryptography For The Financial Services Industry: The
                Elliptic Curve Digital Signature Algorithm (ECDSA)",
                ANSI X9.62, 1998.
 [ANSI-X9.63]   American National Standards Institute, "Public Key
                Cryptography For The Financial Services Industry: Key
                Agreement and Key Transport Using Elliptic Curve
                Cryptography", ANSI X9.63, January 1999.
 [HMV04]        Hankerson, D., Menezes, A., and S. Vanstone, "Guide to
                Elliptic Curve Cryptography", Springer ISBN
                038795273X, 2004.
 [LMQSV98]      Law, L., Menezes, A., Qu, M., Solinas, J., and S.
                Vanstone, "An Efficient Protocol for Authenticated Key
                Agreement", University of Waterloo Technical Report
                CORR 98-05, August 1998, <http://
                www.cacr.math.uwaterloo.ca/techreports/1998/
                corr98-05.pdf>.
 [NIST-800-57]  National Institute of Standards and Technology,
                "Recommendation for Key Management - Part 1: General
                (Revised)", NIST Special Publication 800-57,
                March 2007.
 [NIST-CURVES]  National Institute of Standards and Technology,
                "Recommended Elliptic Curves for Federal Government
                Use", July 1999.

Stebila & Green Standards Track [Page 19] RFC 5656 SSH ECC Algorithm Integration December 2009

Appendix A. Acknowledgements

 The authors acknowledge helpful comments from James Blaisdell, David
 Harrington, Alfred Hoenes, Russ Housley, Jeffrey Hutzelman, Kevin
 Igoe, Rob Lambert, Jan Pechanek, Tim Polk, Sean Turner, Nicolas
 Williams, and members of the ietf-ssh@netbsd.org mailing list.

Authors' Addresses

 Douglas Stebila
 Queensland University of Technology
 Information Security Institute
 Level 7, 126 Margaret St
 Brisbane, Queensland  4000
 Australia
 EMail: douglas@stebila.ca
 Jon Green
 Queen's University
 Parallel Processing Research Laboratory
 Department of Electrical and Computer Engineering
 Room 614, Walter Light Hall
 Kingston, Ontario  K7L 3N6
 Canada
 EMail: jonathan.green@queensu.ca

Stebila & Green Standards Track [Page 20]

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