Secure Shell Working Group J. Green Internet-Draft Certicom Expires: April 19, 2007 D. Stebila U Waterloo October 16, 2006 Elliptic-Curve Algorithm Integration in the Secure Shell Transport Layer draft-green-secsh-ecc-01 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 19, 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 19, 2007 [Page 1] Internet-Draft SSH ECC Algorithm Integration October 2006 Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3. ECC Public Key Algorithm . . . . . . . . . . . . . . . . . . . 5 3.1. Key/Signature Encoding . . . . . . . . . . . . . . . . . . 6 4. ECDH Key Exchange . . . . . . . . . . . . . . . . . . . . . . 7 4.1. Description . . . . . . . . . . . . . . . . . . . . . . . 7 4.2. Implementation . . . . . . . . . . . . . . . . . . . . . . 8 5. ECMQV Key Exchange and Verification . . . . . . . . . . . . . 10 5.1. Description . . . . . . . . . . . . . . . . . . . . . . . 10 5.2. Implementation . . . . . . . . . . . . . . . . . . . . . . 11 6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 14 6.1. ECC Public Key Algorithm Identifiers . . . . . . . . . . . 14 6.2. ECDH Key Exchange Method Names . . . . . . . . . . . . . . 14 6.3. ECMQV Key Exchange and Verification Method Names . . . . . 15 7. Key Exchange Messages . . . . . . . . . . . . . . . . . . . . 16 7.1. ECDH Message Numbers . . . . . . . . . . . . . . . . . . . 16 7.2. ECMQV Message Numbers . . . . . . . . . . . . . . . . . . 16 8. Security Considerations . . . . . . . . . . . . . . . . . . . 17 Appendix A. Named Elliptic Curve Domain Parameters . . . . . . . 18 Appendix A.1. Required and Recommended Curves . . . . . . . . . . 18 Appendix A.2. SEC Equivalent NIST Curves and OIDs . . . . . . . . 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 19, 2007 [Page 2] Internet-Draft SSH ECC Algorithm Integration October 2006 1. Introduction Due to its inclusion in NSA's Suit B and its small key sizes elliptic curve cryptography (ECC) is becoming a widely utilized and attractive public-key cryptosystem. In the interest of adding Suit B algorithms to SSH this document adds three ECC Suit B algorithms to the Secure Shell arsenal: Elliptic Curve Menezes-Qu-Vanstone (ECMQV), Elliptic Curve Diffie-Hellman (ECDH) and Elliptic Curve Digital Signature Algorithm (ECDSA) as well as utilizing the SHA2 family of secure hash algorithms. Compared to 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 [9], 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 | Discrete 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. Implementation of this specification requires familiarity with both SSH [2] [3] [4] and ECC [6] [10] [11]. Green & Stebila Expires April 19, 2007 [Page 3] Internet-Draft SSH ECC Algorithm Integration October 2006 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 RFC 2119 [1]. The data types boolean, uint32, uint64, string, and mpint are to be interpreted in this document as described in RFC 4251 [2]. 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 p. Size on a characteristric-2 curve is defined as the number of bits in the binary representation of the field, commonly denoted m. 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_KEX_ECDH_INIT 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 19, 2007 [Page 4] Internet-Draft SSH ECC Algorithm Integration October 2006 3. ECC Public Key Algorithm 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 server's long term ECC key pair, which are called host keys throughout this draft, is 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 [6] and in [13]. 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 [5] will be used. The algorithm for ECC key generation can be found in section 3.2 of SEC 1 [6]. Given some elliptic curve domain parameters, an ECC key pair can be generated containing an integer d that 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. This public key algorithm only allows named curves, specified by their ASN.1 OIDs, to be used. Details of the curves that are required and recommended are outlined in Appendix A. The family of public key algorithm identifiers for ECC is specified in Section 6.1. For the remainder of this section [identifier] will represent the ECC Public Key Algorithm identifier determined in Section 6.1. Green & Stebila Expires April 19, 2007 [Page 5] Internet-Draft SSH ECC Algorithm Integration October 2006 3.1. Key/Signature Encoding The ecc public key has the following encoding: string [identifier] string Q Where Q is the elliptic curve point that forms the public key. Here Q is encoded from an elliptic curve point into an octet string as defined in Section 2.3.3 of SEC1 [6]. The ECDSA signature has the following encoding: string [identifier] mpint r mpint s Where the integers R and S are the output of the ECDSA algorithm. Green & Stebila Expires April 19, 2007 [Page 6] Internet-Draft SSH ECC Algorithm Integration October 2006 4. ECDH Key Exchange 4.1. Description The Elliptic Curve Diffie-Hellman (ECDH) key exchange algorithm generates a shared secret from an ephemeral elliptic curve private key contributed by the local entity and an ephemeral elliptic curve public key contributed by the remote entity. When this algorithm is applied on both the client and the server both will derive the same shared key. The family of key exchange method names defined for use with this key exchange can be found in Section 6.2. The rest of this section is an informal overview of the ECDH key exchange mechanism. A formal description can be found in Section 4.2. In the following: C is the client, S is the server; NC is the named curve specified in the algorithm name; 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 generates an ephemeral elliptic curve key pair on NC and sends the public-key value 'cPK'. 2. S SHOULD validate 'cPK' using, for example, algorithm A.16.10 of [10]. S generates an ephemeral public-key / private-key pair on NC. 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". 3. C SHOULD validate 'sPK', for example, algorithm A.16.10 of [10]. 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. The size of the named curve specified in the algorithm name 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. Green & Stebila Expires April 19, 2007 [Page 7] Internet-Draft SSH ECC Algorithm Integration October 2006 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 [6]. The algorithm for generation of EC key pairs can be found in Section 3.2 of SEC1 [6]. 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 [6]. The hash algorithm HASH for computing the exchange hash is determined by the size of the named curve specified in the method name. The method for choosing a hash function can be seen in the table below where b is the size of the curve [5]: +----------------+----------------+ | Curve Size | Hash Algorithm | +----------------+----------------+ | b <= 256 | SHA-256 | | | | | 256 < b <= 384 | SHA-384 | | | | | 384 < b | SHA-512 | +----------------+----------------+ Specification of the message numbers SSH_MSG_KEX_ECDH_INIT and SSH_MSG_KEX_ECDH_REPLY are found in Section 7. Green & Stebila Expires April 19, 2007 [Page 8] Internet-Draft SSH ECC Algorithm Integration October 2006 The ECDH key exchange algorithm is implemented with the following messages. The public key algorithm for signing is negotiated with the KEXINIT messages. 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 exchange 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 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 19, 2007 [Page 9] Internet-Draft SSH ECC Algorithm Integration October 2006 5. ECMQV Key Exchange and Verification 5.1. Description The Elliptic Curve Menezes-Qu-Vanstone (ECMQV) key exchange 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 it's key pairs and the other entity's public keys, both entities' will derive the same secret. The family of key exchange method names defined for use with this key exchange can be found in Section 6.3. The following is an informal discussion of ECMQV key exchange and verification for a formal description see Section 5.2. 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 19, 2007 [Page 10] Internet-Draft SSH ECC Algorithm Integration October 2006 In the following: C is the client; S is the server; NC is the curve from the method name; 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. C uses the domain parameters associated with NC to generate an ephemeral ECC public/private key pair. C sends 'cPK'. 2. S SHOULD validate 'cPK' using, for example, algorithm A.16.10 of [10]. S generates an ephemeral public/private key pair using NC. S generates K using its private host key, its private ephemeral key and 'cPK'. S computes H and the message authentication code (MAC) tag 'T' on H using K as the key. S then sends "K_S || sPK || T". 3. C SHOULD 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. 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 [6]. 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 the ECC Public Key Algorithm MUST be selected as the server host key algorithm. This is due to the fact that ECMQV uses the servers ECC host keys within the key exchange. 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 sufficiently strong to ensure that the ECMQV algorithm isn't the weakest point in the SSH encryption suite. Green & Stebila Expires April 19, 2007 [Page 11] Internet-Draft SSH ECC Algorithm Integration October 2006 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 [6]. The hash algorithm HASH 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 [5]: +----------------+----------------+ | 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 verification. The algorithm for implementing HMAC with any of the above hash functions can be found in [5]. The specification of the message numbers 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 [6]. This algorithm is necessary to generate the ephemeral EC key pairs needed for ECMQV. Green & Stebila Expires April 19, 2007 [Page 12] Internet-Draft SSH ECC Algorithm Integration October 2006 This key exchange algorithm is implemented with the following messages. The client sends: 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 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 19, 2007 [Page 13] Internet-Draft SSH ECC Algorithm Integration October 2006 6. IANA Considerations This document defines two new families of key exchange method names and one new family of public key algorithm name in the SSH name registry. These additions to the SSH name space will have to be approved the IANA. The specification of these families is found below. 6.1. ECC Public Key Algorithm Identifiers The ECC Public Key Algorithm specifies a family of identifiers. The general format for this family of identifiers is the string "secg- ecc-" concatenated with the ASN.1 OID, in dotted decimal format, of the named curve domain parameters that are associated with the server's ECC host keys [8]. There are two other identifiers in the ECC Public Key family that are only to be used only by the client during algorithm negotiation in SSH_MSG_KEXINIT messages. These identifiers can: not be used at all, used on their own, or used in concert with normal "secg-ecc-[oid]" identifiers to specify additional supported named curves that the are not included in the special identifiers. "secg-ecc-standard" tells the server that the clients local security policy has not disabled any of the required curves specified in Appendix A and is analogous to sending "secg-ecc-1.3.132.0.37,secg- ecc-1.3.132.0.34,secg-ecc-1.3.132.0.16,secg-ecc-1.2.840.10045.3.1.7". "secg-ecc-extended" tells the server that the client supports all of the curves specified in Appendix A and is analogous to sending "secg- ecc-1.3.132.0.38,secg-ecc-1.3.132.0.35,secg-ecc-1.3.132.0.37,secg- ecc-1.3.132.0.36,secg-ecc-1.3.132.0.34,secg-ecc-1.3.132.0.16,secg- ecc-1.2.840.10045.3.1.7,secg-ecc-1.3.132.0.27,secg-ecc- 1.3.132.0.26,secg-ecc-1.3.132.0.33,secg-ecc-1.2.840.10045.3.1.1,secg- ecc-1.3.132.0.1". 6.2. ECDH Key Exchange Method Names The Elliptic Curve Diffie-Hellman key exchange is defined by a family of method names. Each method name consists of the string "ecdh- sha2-" concatenated with the ASN.1 OID of the named curve, in dotted decimal notation, to be used for ephemeral key generation within the key exchange algorithm [8]. Information on the named curves that are required and recommended can be found in Appendix A. Green & Stebila Expires April 19, 2007 [Page 14] Internet-Draft SSH ECC Algorithm Integration October 2006 6.3. ECMQV Key Exchange and Verification Method Names The Elliptic Curve Menezes-Qu-Vanstone key exchange is defined by a family of method names that specify what named curve will be used within the key exchange. Each method name consists of the string "ecmqv-sha2-" concatenated with the ASN.1 OID of the named curve to be used in dotted decimal notation. Information on the named curves that are required and recommended can be found in Appendix A [8]. When the server forms its 'server_host_key_algorithms' name-list it MUST include only the algorithm from the "ecmqv-sha2-*" family that corresponds to the named curve used to produce its ECC host keys. If the server doesn't have an ECC host key then the server MUST NOT put any members of the "ecmqv-sha2-*" family of algorithms in the 'server_host_key_algorithms' name-list. Green & Stebila Expires April 19, 2007 [Page 15] 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 [4] that may be redefined by any key exchange method [3] 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_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 Green & Stebila Expires April 19, 2007 [Page 16] Internet-Draft SSH ECC Algorithm Integration October 2006 8. Security Considerations The Elliptic Curve Diffie-Hellman key agreement algorithm is defined in [6], [10] and [11]. The appropriate security considerations of those documents apply. The Elliptic Curve Menezes-Qu-Vanstone key agreement algorithm is defined in [6]. 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 [14]. The methods defined in Section 4 rely on the SHA family of hashing functions as defined in [15]. 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 [14]. 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 [9]. Green & Stebila Expires April 19, 2007 [Page 17] 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 [8]. Appendix A.1. Required and Recommended Curves Every SSH ECC implementation MUST support the named curves below, these curves are defined in SEC2 [7]. These curves should always be enabled unless specifically disabled by local security policy. 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. SEC Equivalent NIST Curves and OIDs +-----------+----------+---------------------+ | SEC | NIST[12] | OID[7] | +-----------+----------+---------------------+ | sect163k1 | nistk163 | 1.3.132.0.1 | | | | | | secp192r1 | nistp192 | 1.2.840.10045.3.1.1 | | | | | | secp224r1 | nistp224 | 1.3.132.0.33 | | | | | | sect233k1 | nistk233 | 1.3.132.0.26 | | | | | | sect233r1 | nistb233 | 1.3.132.0.27 | | | | | | secp256r1 | nistp256 | 1.2.840.10045.3.1.7 | | | | | | sect283k1 | nistk283 | 1.3.132.0.16 | | | | | | secp384r1 | nistp384 | 1.3.132.0.34 | | | | | | sect409k1 | nistk409 | 1.3.132.0.36 | | | | | | sect409r1 | nistb409 | 1.3.132.0.37 | | | | | | secp521r1 | nistp521 | 1.3.132.0.35 | | | | | | sect571k1 | nistk571 | 1.3.132.0.38 | +-----------+----------+---------------------+ Green & Stebila Expires April 19, 2007 [Page 18] Internet-Draft SSH ECC Algorithm Integration October 2006 9. Acknowledgements Douglas Stebila wishes to thank Sheueling Chang and Vipul Gupta of Sun Microsystems. The work on draft-stebila-secsh-ecdh-01, of which this work is a derivative document, was largely performed during a student internship at Sun Microsystems Laboratories from the University of Waterloo. Jon Green would like to thank Robert Lambert of Certicom for all the help and knowledge he provided. This document was written during an internship at Certicom from Queens University. Green & Stebila Expires April 19, 2007 [Page 19] Internet-Draft SSH ECC Algorithm Integration October 2006 10. References 10.1. Normative References [1] Bradner, S., "Key Words for Use in RFCs to Indicate Requirement Levels", RFC 2119, March 1997. [2] Ylonen, T. and C. Lonvick, Ed., "The Secure Shell Protocol Architecture", RFC 4251, January 2006. [3] Ylonen, T. and C. Lonvick, Ed., "The Secure Shell Transport Layer Protocol", RFC 4253, January 2006. [4] Lehtinen, S. and C. Lonvick, Ed., "The Secure Shell Protocol Assigned Numbers", RFC 4250, January 2006. [5] Eastlake, 3rd, D. and T. Hansen, "US Secure Hash Algorithms (SHA and HMAC-SHA)", RFC 4634, July 2006. [6] Standards for Efficient Cryptography Group, "Elliptic Curve Cryptography", SEC 1 v1.0, September 2000. [7] Standards for Efficient Cryptography Group, "Recommended Elliptic Curve Domain Parameters", SEC 2 v1.0, September 2000. [8] International Telecommunication Union, "Abstract Syntax Notation One (ASN.1): Specification of basic notation", X.680 , July 2002. Green & Stebila Expires April 19, 2007 [Page 20] Internet-Draft SSH ECC Algorithm Integration October 2006 10.2. Informative References [9] National Institute of Standards and Technology, "Recommendation for Key Management - Part 1", NIST Special Publication 800-57. [10] Institute of Electrical and Electronics Engineers, "Standard Specifications for Public Key Cryptography", IEEE 1363, 2000. [11] 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. [12] National Institute of Standards and Technology, "Recommended Elliptic Curves for Federal Government Use", August 1999. [13] American National Standards Institute, "Public Key Cryptography For The Financial Services Industry The Elliptic Curve Digital Signature Algorithm", ANSI X9.62, 1998. [14] Hankerson, Menezes, and Vanstone, "Guide to Elliptic Curve Cryptography", 2004, . [15] National Institute of Standards and Technology, "Secure Hash Standard", FIPS 180-2, August 2002. Green & Stebila Expires April 19, 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 19, 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. 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