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SSH in ECC Internet Draft



In the interest of supporting the US government's Suite B cryptographic
algorithms, we have updated an ECC in SSH draft written by D. Stabila
(draft-stebila-secsh-ecdh-01) and have added Suite B algorithms,
specifically MQV to the draft.

This draft has been submitted to the IETF as an internet draft and I'm
posting it on this list to solicit some review and to try to generate
some interest. Any comments on the draft at all would be appreciated. 

Thanks
--
Jon Green
Research Intern
Certicom Corp.


Secure Shell Working Group                                      J. Green
Internet-Draft                                                  Certicom
Expires: April 8, 2007                                        D. Stebila
                                                              U Waterloo
                                                         October 5, 2006


Elliptic-Curve Algorithm Integration in the Secure Shell Transport Layer
                        draft-green-secsh-ecc-00

Status of this Memo

   By submitting this Internet-Draft, each author represents that any
   applicable patent or other IPR claims of which he or she is aware
   have been or will be disclosed, and any of which he or she becomes
   aware will be disclosed, in accordance with Section 6 of BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
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   The list of current Internet-Drafts can be accessed at
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   http://www.ietf.org/shadow.html.

   This Internet-Draft will expire on April 8, 2007.

Copyright Notice

   Copyright (C) The Internet Society (2006).

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.




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Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
   2.  Requirements Notation  . . . . . . . . . . . . . . . . . . . .  4
   3.  ECC Public Key Algorithm [ssh-ecc] . . . . . . . . . . . . . .  5
     3.1.  Key/Signature Encoding . . . . . . . . . . . . . . . . . .  6
   4.  ECDH Parameter and Key Exchange [ecdh-exchange]  . . . . . . .  7
     4.1.  Description  . . . . . . . . . . . . . . . . . . . . . . .  7
     4.2.  Implementation . . . . . . . . . . . . . . . . . . . . . .  8
   5.  ECMQV Key Exchange and Verification [ecmqv]  . . . . . . . . . 10
     5.1.  Description  . . . . . . . . . . . . . . . . . . . . . . . 10
     5.2.  Implementation . . . . . . . . . . . . . . . . . . . . . . 11
   6.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 14
     6.1.  ssh-ecc  . . . . . . . . . . . . . . . . . . . . . . . . . 14
     6.2.  ecdh-exchange  . . . . . . . . . . . . . . . . . . . . . . 14
     6.3.  ecmqv  . . . . . . . . . . . . . . . . . . . . . . . . . . 14
   7.  Key Exchange Messages  . . . . . . . . . . . . . . . . . . . . 15
     7.1.  ECDH Message Numbers . . . . . . . . . . . . . . . . . . . 15
     7.2.  ECMQV Message Numbers  . . . . . . . . . . . . . . . . . . 15
   8.  Security Considerations  . . . . . . . . . . . . . . . . . . . 16
   Appendix A.   Named Elliptic Curve Domain Parameters . . . . . . . 17
   Appendix A.1. Required and Recommended Curves  . . . . . . . . . . 17
   Appendix A.2. Sending Lists of Curves  . . . . . . . . . . . . . . 17
   Appendix A.3. SEC Equivalent NIST Curves . . . . . . . . . . . . . 18
   9.  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 19
   10. References . . . . . . . . . . . . . . . . . . . . . . . . . . 20
     10.1. Normative References . . . . . . . . . . . . . . . . . . . 20
     10.2. Informative References . . . . . . . . . . . . . . . . . . 21
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 22
   Intellectual Property and Copyright Statements . . . . . . . . . . 23





















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1.  Introduction

   Elliptic Curve Cryptography (ECC) is emerging as an attractive
   public-key cryptosystem for environments with limited bandwidth and
   computing power.  Compared to currently prevalent cryptosystems such
   as RSA, DSA, and DH, 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 [11], which
   gives approximate comparable key sizes for symmetric- and asymmetric-
   key cryptosystems based on the best known algorithms for attacking
   them.  L is field size and N is sub-field size.

       +-----------+-----------------------------+-------+---------+
       | Symmetric |  Discreet Log (eg. 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+  |
       +-----------+-----------------------------+-------+---------+

                 Figure 1: Comparable key sizes (in bits).

   Smaller key sizes result in power, bandwidth, and computational
   savings that make ECC especially attractive for constrained
   environments.

   This document describes additions to the SSH transport layer to
   support the use of Elliptic Curve Digital Signature Algorithm (ECDSA)
   for message signing, Elliptic Curve Diffie-Hellman (ECDH) and
   Elliptic Curve Menezes-Qu-Vanstone (ECMQV) to establish a shared key.

   Implementation of this specification requires familiarity with both
   SSH [1] [2] [3] and ECC [4] [12] [13].
   
   Comments on this draft are solicited and should be addressed to
   Jon Green <jgreen%certicom.com@localhost>.









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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 RFC 2119 [6].

   The data types boolean, uint32, uint64, string, and mpint are to be
   interpreted in this document as described in RFC 4251 [1].

   This document uses Abstract Syntax Notation (ASN.1) define some
   communication.  This is in keeping with current ECC standards.  All
   ASN.1 variables are DER encoded before being sent.  Information about
   the ASN.1 and DER can be found in ITU-T recommendation X.680 [7] and
   ITU-T recommendation X.690 [8].

   Protocol fields and possible values to fill them in are defined in
   this set of documents.  As an example SSH_MSG_KEX_ECDH_INIT is
   defined as follows.

      byte       SSH_MSG_NUMBER
      string     pK, public key octet string.

   Throughout these documents, when the fields are referenced, they will
   appear within single quotes.  When values to fill in those fields are
   referenced they will appear in double quotes.


























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3.  ECC Public Key Algorithm [ssh-ecc]

   The ECC public key algorithm defines ECC public keys, private keys
   and signatures for use within the SSH protocol.  When ECC is chosen
   as the public key algorithm through key exchange negotiations the
   servers long term ECC key pair (host keys) are used for
   identification and verification.

   When asked to sign communications or verify signatures by the key
   exchange method the elliptic curve digital signature algorithm
   (ECDSA) is used.  The algorithmic details of ECDSA can be found in
   Section 4 of SEC 1 [4] and in [15].  This document is concerned with
   the SSH implementation details, specification of the algorithm is
   left to other standards documents.

   The message hashing algorithm to be used with ECDSA is the same one
   specified to generate the exchange hash in the key exchange method
   chosen during algorithm negotiation.  If the chosen key exchange
   method doesn't specify a hashing function then SHA-256 [9] will be
   used.

   The algorithm for ECC key generation can be found in section 3.2 of
   SEC 1 [4].  Given some elliptic curve domain parameters, an ECC key
   pair can be generated containing an integer d that is makes up the
   secret key and an elliptic curve point Q which makes up the public
   key.

   The elliptic curve domain parameters to generate EC keys can be
   produced at random, but this is a costly operation and may result in
   the use of domain parameters of which the security hasn't been
   tested.  Because of this, standards bodies have produced named sets
   of elliptic curve domain parameters or named curves.  Details of the
   curves required and recommended by this public key algorithm are
   outlined in Appendix A.

   The public key algorithm identifier specified for ECC is "ssh-ecc".
   This specification conforms to conventions for the SSH public key
   algorithm namespace [2] and must be approved by the IANA before it is
   put into use.












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3.1.  Key/Signature Encoding

   The ECC public key and signature are sent in the standard encoding
   for ECC keys and signatures.  This requires ASN.1 DER encoding which
   is specified in [7] and [8].

   The ecc public key has the following encoding:

      string     "ssh-ecc"
      ASN/DER    SubjectPublicKeyInfo

   Here 'SubjectPublicKeyInfo' is defined as it is in Section C3 of SEC1
   [4].

   The ecdsa signature has the following encoding:

      string     "ssh-ecc"
      ASN/DER    ECDSA-Sig-Value

   Here the integers R and S that form the ECDSA signature are
   encapsulated in the ASN.1 field 'ECDSA-Sig-Value'.  The field 'ECDSA-
   Sig-Value' is defined here as it is in Section C6 of SEC1 [4].





























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4.  ECDH Parameter and Key Exchange [ecdh-exchange]

4.1.  Description

   This section is an informal overview of the elliptic curve Diffie-
   Hellman (ECDH) key exchange mechanism.  A formal description can be
   found in Section 4.2.

   The first stage of the ECDH key exchange mechanism is the exchange of
   elliptic curve domain parameters.

   Once the domain parameters are decided upon, both the client and
   server generate ephemeral EC key pairs, and exchange their ephemeral
   public keys.  Using its own key pair and the other's public key both
   the client and the server derive the same shared secret key using
   ECDH.

   In the following: C is the client, S is the server; E_C is the
   client's list of supported curves; E_S is the server's list of
   supported curves; cPK is the client's ephemeral public key; sPK is
   the server's ephemeral public key; K_S is the server's public host
   key; H is the exchange hash; s is the signature on H; and K is the
   shared secret.

   1.  C and S send 'E_C' and 'E_S', lists ordered by preference (most
       to least) of named elliptic curve domain parameters.  The first
       curve in 'E_C' that also appears in 'E_S' is the curve that will
       be used for ephemeral key generation.  If there are no matching
       curves both sides MUST disconnect.

   2.  C chooses the curve it prefers most from from 'E_S' then
       generates an ephemeral elliptic curve public-key / private-key
       pair and sends the public-key value 'cPK'.

   3.  S MAY validate 'cPK' using for example algorithm A.16.10 of [12].
       S chooses the first curve in 'E_C' it supports and uses it to
       generate an ephemeral public-key / private-key pair.  S uses cPK
       and S's ephemeral private key value to compute the shared secret
       K using ECDH.  S computes 'H' and the signature 's' on 'H' using
       its private host key.  S sends "K_S || sPK || s".

   4.  C MAY validate S's public-key value using for example algorithm
       A.16.10 of [12].  C verifies that 'K_S' really is the public host
       key for S (e.g., using certificates or a local database).  C is
       also allowed to accept the key without verification; however,
       doing so will render the protocol insecure against active
       attacks.  C uses 'sPK' and C's ephemeral private key to compute
       the shared secret and verifies the signature 's' on 'H'.



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   The size of the selected curve SHOULD be greater than 160 bits, and
   preferably at least 224 bits.  The size of the curve used SHOULD be
   in line with the bulk encryption algorithm chosen during algorithm
   negotiation.  Appendix A contains more information about required and
   recommended curves.

4.2.  Implementation

   This document is concerned with describing the implementation of ECDH
   in SSH, not the specification of the algorithm itself.  The algorithm
   used for shared key generation is ECDH, the full specification of
   which can be found in Section 3.3.2 of SEC1 [4].

   The algorithm for generation of EC key pairs can be found in Section
   3.2 of SEC1 [4].  This algorithm is necessary to generate the
   ephemeral EC key pairs needed for ECDH.

   The elliptic curve points (ephemeral public keys) 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 SEC1 Section 2.3 [4].

   The hash algorithm for computing the exchange hash is determined by
   the size of the named curve chosen.  The method for choosing a hash
   function can be seen in the table below where b is the size of the
   curve:

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















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   Specification of the message numbers SSH_MSG_KEX_ECDH_REQUEST,
   SSH_MSG_KEX_ECDH_INIT and SSH_MSG_KEX_ECDH_REPLY are found in
   Section 7.

   The ECDH key exchange algorithm is implemented with the following
   messages.  The public key algorithm for signing is negotiated with
   the KEXINIT messages.
   
   Both the client and server send:

   byte       SSH_MSG_KEX_ECDH_REQUEST
   ASN/DER    curves (E_C or E_S), the list of supported curves

      Information on the ASN.1 syntax used for curves can be found in
      Appendix A.2.

   The client sends:

   byte       SSH_MSG_KEX_ECDH_INIT
   string     cPK, the octet string formed from the
              client's ephemeral public key.

   The server responds with:

   byte       SSH_MSG_KEX_ECDH_REPLY
   string     K_S, server public host key and/or certificates
   string     sPK, the octet string formed from the server's
              ephemeral public key.
   string     s, the signature of H

   The hash H is computed as the 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 server's public host key
   ASN/DER    E_C, the client's supported curve list
   ASN/DER    E_S, the server's supported curve list
   string     cPK, the client's ephemeral public key octet string.
   string     sPK, the server's ephemeral public key octet string.
   mpint      K, the shared secret







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5.  ECMQV Key Exchange and Verification [ecmqv]

5.1.  Description

   The Elliptic Curve Menezes-Qu-Vanstone (ECMQV) key generation
   algorithm generates a shared secret from two elliptic curve key pairs
   owned by one entity and two elliptic curve public keys owned by
   another entity.  Both entities roles are analogous in the algorithm.
   Using their own key pairs and the other entities public keys, both
   will derive the same secret.

   The following is an informal discussion of ECMQV key exchange and
   verification for a formal description see Section 5.2.

   The key exchange starts with the communication, from the server to
   the client, of the named curve that will be used for ephemeral key
   generation.  The server and the client generate ephemeral key pairs,
   and exchange their public keys and use the ECMQV algorithm to derive
   the shared key.

   The client doesn't necessarily have a long term key under the
   existing SSH protocol.  Instead of generating two ephemeral key pairs
   the client generates one ephemeral key pair and uses it for all the
   keys it is required to supply.  This is illustrated below considering
   the ECMQV algorithm in terms of a black box:

          Local Keys      |-----|-|-----|      Remote Keys

   ECMQV Block:               _______
                Key Pair ----|       |---- Public Key
                             | ECMQV |
                Key Pair ----|_______|---- Public Key
                                 |
                           shared secret

   Server Configuration:      _______
      Server Host Key    ----|       |----
             Pair            | ECMQV |   |--  Client Ephemeral
    Server Ephemeral Key ----|_______|----      Public Key
             Pair                |
                           shared secret

   Client Configuration:      _______
                         ----|       |---- Server Public Host Key
      Client Ephemeral --|   | ECMQV |
          Key Pair       ----|_______|---- Server Ephemeral Public
                                 |                   Key
                           shared secret



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   In the following: C is the client; S is the server; curve is the
   curve used to generate the host key; K_S is the server's public host
   key; sPK is the server's ephemeral public key; cPK is the client's
   ephemeral public key; H is the exchange hash; T is the HMAC tag of H;
   and K is the shared secret.

   1.  S sends 'curve' containing the named curve that was used to
       generate its ECC host keys.

   2.  C OPTIONALLY verifies that the 'curve' has an acceptable level of
       security compared to the bulk encryption algorithm chosen during
       algorithm negotiation, a good reference for key strength
       comparison can be found in [11].  If C accepts 'curve' then it
       uses the associated domain parameters to generate an ephemeral
       ECC public/private key pair.  C sends 'cPK'.

   3.  S MAY validate 'cPK' using, for example, algorithm A.16.10 of
       [12].  S generates an ephemeral public/private key pair using
       'curve'.  S then generates 'K' using its private hostkey, its
       private ephemeral key and 'cPK'.  S computes 'H' (specified
       below) and the message authentication code (MAC) tag 'T' =
       HMAC(K,H).  S then sends "K_S || sPK || T".

   4.  C MAY validate 'sPK' and 'K_S' as above.  C verifies that 'K_S'
       really is the public host key for S (e.g., using certificates or
       a local database).  C is also allowed to accept the key without
       verification; however, doing so will render the protocol insecure
       against active attacks.  C generates 'K' using its private
       ephemeral key, 'sPK' and 'K_S'.  C independently computes 'H' and
       verifies the tag 'T' is valid for its 'H' and 'K'.  We use a MAC
       tag with 'K' as a key for verification of communication with S
       because the private host key was used to create 'K', eliminating
       the need for a costly signing algorithm.

5.2.  Implementation

   This document is concerned with describing the implementation of
   ECMQV in SSH, not the specification of the algorithm itself.  A full
   description of ECMQV can be found in Section 3.4 of SEC1 [4].

   An implementation of SSH supporting ECMQV MUST support the ECC Public
   Key Algorithm (Section 3).  If during the key exchange algorithm
   negotiation ECMQV is chosen as the key exchange algorithm then "ssh-
   ecc" MUST be selected as the server host key algorithm.  If "ssh-ecc"
   is not in the clients name-list then both sides MUST disconnect.






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   ECMQV Key Exchange relies on the ECC public key algorithm to provide
   it with the necessary ECC server host key.  ECMQV should support the
   same set of curves that the ECC public key algorithm supports.
   Required and recommended curve support is outlined in Appendix A.

   The server's host keys are used in shared key generation, therefore
   the named curve used to generate them is the curve that must be used
   by the ECMQV algorithm.  Care should be taken that the server's host
   key is generated with sufficient strength to ensure that the ECMQV
   algorithm isn't the weakest point in the SSH encryption suite.

   The elliptic curve points (public keys) 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 SEC1 Section 2.3 [4].

   The hash algorithm for computing the exchange hash is determined by
   the strength of the named curve used by ECMQV.  The method for
   choosing a hash function can be seen in the table below where b is
   the size of the curve:

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

   The hash function chosen above is also the hash function that is used
   to implement the HMAC used for server identification and
   varification.  The algorithm for implementing HMAC with any of the
   above hash functions can be found in [10].

   The specificiation of the message numbers SSH_MSG_ECMQV_KEYTYPE,
   SSH_MSG_ECMQV_INIT and SSH_MSG_ECMQV_REPLY can be found in Section 7.

   The algorithm for generation of EC key pairs can be found in SEC1
   Section 3.2 [4].  This algorithm is necessary to generate the
   ephemeral EC key pairs needed for ECMQV.









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   This key exchange algorithm is implemented with the following
   messages.

   The server sends:

   byte        SSH_MSG_ECMQV_KEYTYPE
   ASN/DER     curve
   
      Information on the ASN.1 syntax used for curve can be found in
      Appendix A.

   The client responds with:

   byte       SSH_MSG_ECMQV_INIT
   string     cPK, The octet string formed from the client's
              ephemeral public key.

   The server sends:

   byte       SSH_MSG_ECMQV_REPLY
   string     K_S, Server public host key octet string
   string     sPK, Server ephemeral public key octet string
   string     T, The 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, 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
   ASN/DER    curve, the named curve all the keys are based upon
   string     cPK, client's ephemeral public key octet
   string     K_S, server's public host key octet
   string     sPK, server's ephemeral public key octet
   mpint      K, the shared secret















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6.  IANA Considerations

   This document defines two new key exchange method names and one new
   public key algorithm name in the SSH name registry.  These additions
   to the SSH namespace will have to be approved by the IANA.

   New Key Exchange Algorithms:

         "ecmqv"
         "ecdh-exchange"

   New Host Key Algorithms:

         "ssh-ecc"

6.1.  ssh-ecc

   The "ssh-ecc" method specifies Elliptic Curve digital signature
   algorithm (ECDSA) for use in signing communications with ECC host
   keys.  When used with ECMQV "ssh-ecc" provides ecmqv with a host key.
   This method is discussed in Section 3.

6.2.  ecdh-exchange

   The "ecdh-exchange" method specifies Elliptic Curve Diffie-Hellman
   with for key exchange as described in Section 4.

6.3.  ecmqv

   The "ecmqv" method specifies the use of Elliptic Curve Menezes-Qu-
   Vanstone for Key Exchange as discussed in Section 5.




















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7.  Key Exchange Messages

   The message numbers 30-49 are key exchange-specific and in a private
   namespace defined in RFC4250 [3] that may be redefined by any key
   exchange method [2] without being granted IANA permission.

   The following message numbers have been defined in this document:

7.1.  ECDH Message Numbers

   #define SSH_MSG_KEX_ECDH_REQUEST             30
   #define SSH_MSG_KEX_ECDH_INIT                31
   #define SSH_MSG_KEX_ECDH_REPLY               32

7.2.  ECMQV Message Numbers

   #define SSH_MSG_ECMQV_KEYTYPE                30
   #define SSH_MSG_ECMQV_INIT                   31
   #define SSH_MSG_ECMQV_REPLY                  32
































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8.  Security Considerations

   The Elliptic Curve Diffie-Hellman key agreement algorithm is defined
   in [4], [12] and [13].  The appropriate security considerations of
   those documents apply.

   The Elliptic Curve Menezes-Qu-Vanstone key agreement algorithm is
   defined in [4].  The security considerations raised in that document
   also apply.  A more detailed discussion of security considerations
   can be found in The Guide to Elliptic Curve Cryptography section 4.7
   [16].

   The methods defined in Section 4 rely on the SHA family of hashing
   functions as defined in [9].  The appropriate security considerations
   of that document apply.

   Additionally a good general discussion of the security considerations
   that must be taken into account when creating an ECC implementation
   can be found in The Guide to Elliptic Curve Cryptography section 5
   [16].

   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 [11].























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Appendix A.  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.  Curve is defined in ASN.1 syntax below.

   curve ::= OBJECT IDENTIFIER UNIQUE

Appendix A.1.  Required and Recommended Curves

   Every SSH ECC implementation MUST support the named curves below,
   these curves are defined in SEC2 [5].

         secp256r1    sect283k1    secp384r1    sect409k1

   It is RECOMMENDED that SSH ECC implementations also support the
   following curves.

         sect163k1    secp192r1    sect233k1    secp224r1
         sect233r1    sect409r1    secp521r1    sect571k1

Appendix A.2.  Sending Lists of Curves

   When lists of curves need to be sent to negotiate mutually supported
   curves they are sent as a sequence of unique ASN.1 OIDS.  The ASN.1
   syntax of this curve list is shown below.  This ASN.1 syntax is
   encoded with DER and put into the appropriate packet.

   curves::= SEQUENCE SIZE (1 ... 12) OF { curve }






















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Appendix A.3.  SEC Equivalent NIST Curves

                         +-----------+----------+
                         |    SEC    | NIST[14] |
                         +-----------+----------+
                         | sect163k1 | nistk163 |
                         |           |          |
                         | secp192r1 | nistp192 |
                         |           |          |
                         | secp224r1 | nistp224 |
                         |           |          |
                         | sect233k1 | nistk233 |
                         |           |          |
                         | sect233r1 | nistb233 |
                         |           |          |
                         | secp256r1 | nistp256 |
                         |           |          |
                         | sect283k1 | nistk283 |
                         |           |          |
                         | secp384r1 | nistp384 |
                         |           |          |
                         | sect409k1 | nistk409 |
                         |           |          |
                         | sect409r1 | nistb409 |
                         |           |          |
                         | secp521r1 | nistp521 |
                         |           |          |
                         | sect571k1 | nistk571 |
                         +-----------+----------+

   OIDs for the above curves can be found in SEC2 Section A.2.1 and
   A.2.2 [5].



















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9.  Acknowledgements

   The author would like to thank Douglas Stebila who wrote
   draft-stebila-secsh-ecdh-01, the ECDH portion of this draft is
   largely an updated version of his document.
   
   The author would also like to thank Robert Lambert of Certicom
   for all the help and knowledge he provided. 
   
   This work was performed during an internship at Certicom from 
   Queens University.







































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10.  References

10.1.  Normative References

   [1]   Ylonen, T. and C. Lonvick, Ed., "The Secure Shell Protocol
         Architecture", RFC 4251, January 2006.

   [2]   Ylonen, T. and C. Lonvick, Ed., "The Secure Shell Transport
         Layer Protocol", RFC 4253, January 2006.

   [3]   Lehtinen, S. and C. Lonvick, Ed., "The Secure Shell Protocol
         Assigned Numbers", RFC 4250, January 2006.

   [4]   Standards for Efficient Cryptography Group, "Elliptic Curve
         Cryptography", SEC 1, September 2000.

   [5]   Standards for Efficient Cryptography Group, "Recommended
         Elliptic Curve Domain Parameters", SEC 2, September 2000.

   [6]   Bradner, S., "Key Words for Use in RFCs to Indicate Requirement
         Levels", RFC 2119, March 1997.

   [7]   Internation Telecommunication Union, "Abstract Syntax Notation
         One (ASN.1): Specification of basic notation", X. 680,
         July 2002.

   [8]   Internation Telecommunication Union, "ASN.1 encoding rules",
         X. 690, July 2002.

   [9]   National Institute of Standards and Technology, "Secure Hash
         Standard", FIPS 180-2, August 2002.

   [10]  National Institute of Standards and Technology, "Keyed-Hash
         Message Authentication Code", FIPS 198, March 2002.

















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10.2.  Informative References

   [11]  National Institute of Standards and Technology, "Recommendation
         for Key Management - Part 1", NIST Special Publication 800-57.

   [12]  Institute of Electrical and Electronics Engineers, "Standard
         Specifications for Public Key Cryptography", IEEE 1363, 2000.

   [13]  American National Standards Institute, "Public Key Cryptography
         For The Financial Services Industry: Key Agreement and key
         Transport Using Elliptic Curve Cryptography", ANSI X9.63,
         November 2001.
         
   [14]  National Institute of Standards and Technology, "Recommended
         Elliptic Curves for Federal Government Use", August 1999.

   [15]  American National Standards Institute, "Public Key Cryptography
         For The Financial Services Industry The Elliptic Curve Digital
         Signature Algorithm", ANSI X9.62, 1998.

   [16]  Hankerson, Menezes, and Vanstone, "Guide to Elliptic Curve
         Cryptography", 2004, <urn:isbn:038795273X>.





























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Authors' Addresses

   Jon Green
   Certicom
   5520 Explorer Drive
   4th Floor
   Mississauga, ON  L4W 5L1
   Canada

   Email: jgreen%certicom.com@localhost


   Douglas Stebila
   Department of Combinatorics and Optimization
   University of Waterloo
   Waterloo, ON  N2L 3G1
   Canada

   Email: douglas%stebila.ca@localhost
































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