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 Task Force (IETF), its areas, and its working groups. Note that other groups may also distribute working documents as Internet- Drafts. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." The list of current Internet-Drafts can be accessed at http://www.ietf.org/ietf/1id-abstracts.txt. The list of Internet-Draft Shadow Directories can be accessed at 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. Green & Stebila Expires April 8, 2007 [Page 1]

Internet-Draft SSH ECC Algorithm Integration October 2006 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 Green & Stebila Expires April 8, 2007 [Page 2]

Internet-Draft SSH ECC Algorithm Integration October 2006 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>. Green & Stebila Expires April 8, 2007 [Page 3]

Internet-Draft SSH ECC Algorithm Integration October 2006 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. Green & Stebila Expires April 8, 2007 [Page 4]

Internet-Draft SSH ECC Algorithm Integration October 2006 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. Green & Stebila Expires April 8, 2007 [Page 5]

Internet-Draft SSH ECC Algorithm Integration October 2006 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]. Green & Stebila Expires April 8, 2007 [Page 6]

Internet-Draft SSH ECC Algorithm Integration October 2006 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'. Green & Stebila Expires April 8, 2007 [Page 7]

Internet-Draft SSH ECC Algorithm Integration October 2006 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 | +----------------+----------------+ Green & Stebila Expires April 8, 2007 [Page 8]

Internet-Draft SSH ECC Algorithm Integration October 2006 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 Green & Stebila Expires April 8, 2007 [Page 9]

Internet-Draft SSH ECC Algorithm Integration October 2006 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 Green & Stebila Expires April 8, 2007 [Page 10]

Internet-Draft SSH ECC Algorithm Integration October 2006 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. Green & Stebila Expires April 8, 2007 [Page 11]

Internet-Draft SSH ECC Algorithm Integration October 2006 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. Green & Stebila Expires April 8, 2007 [Page 12]

Internet-Draft SSH ECC Algorithm Integration October 2006 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 Green & Stebila Expires April 8, 2007 [Page 13]

Internet-Draft SSH ECC Algorithm Integration October 2006 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. Green & Stebila Expires April 8, 2007 [Page 14]

Internet-Draft SSH ECC Algorithm Integration October 2006 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 Green & Stebila Expires April 8, 2007 [Page 15]

Internet-Draft SSH ECC Algorithm Integration October 2006 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]. Green & Stebila Expires April 8, 2007 [Page 16]

Internet-Draft SSH ECC Algorithm Integration October 2006 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 } Green & Stebila Expires April 8, 2007 [Page 17]

Internet-Draft SSH ECC Algorithm Integration October 2006 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]. Green & Stebila Expires April 8, 2007 [Page 18]

Internet-Draft SSH ECC Algorithm Integration October 2006 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. Green & Stebila Expires April 8, 2007 [Page 19]

Internet-Draft SSH ECC Algorithm Integration October 2006 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. Green & Stebila Expires April 8, 2007 [Page 20]

Internet-Draft SSH ECC Algorithm Integration October 2006 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>. Green & Stebila Expires April 8, 2007 [Page 21]

Internet-Draft SSH ECC Algorithm Integration October 2006 Authors' Addresses Jon Green Certicom 5520 Explorer Drive 4th Floor Mississauga, ON L4W 5L1 Canada Email: jgreen@certicom.com Douglas Stebila Department of Combinatorics and Optimization University of Waterloo Waterloo, ON N2L 3G1 Canada Email: douglas@stebila.ca Green & Stebila Expires April 8, 2007 [Page 22]

Internet-Draft SSH ECC Algorithm Integration October 2006 Intellectual Property Statement 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 in BCP 78 and BCP 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 at http://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. Disclaimer of Validity 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. Copyright Statement Copyright (C) The Internet Society (2006). This document is subject to the rights, licenses and restrictions contained in BCP 78, and except as set forth therein, the authors retain all their rights. Acknowledgment Funding for the RFC Editor function is currently provided by the Internet Society. Green & Stebila Expires April 8, 2007 [Page 23]