Network Working Group Y. Nir Internet-Draft Check Point Intended status: Standards Track S. Josefsson Expires: March 3, 2017 SJD August 30, 2016 Curve25519 and Curve448 for IKEv2 Key Agreement draft-ietf-ipsecme-safecurves-04 Abstract This document describes the use of Curve25519 and Curve448 for ephemeral key exchange in the Internet Key Exchange (IKEv2) protocol. Status of This Memo This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet- Drafts is at http://datatracker.ietf.org/drafts/current/. 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." This Internet-Draft will expire on March 3, 2017. Copyright Notice Copyright (c) 2016 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License. Nir & Josefsson Expires March 3, 2017 [Page 1] Internet-Draft Curve25519 and Curve448 for IKEv2 August 2016 Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1. Conventions Used in This Document . . . . . . . . . . . . 2 2. Curve25519 & Curve448 . . . . . . . . . . . . . . . . . . . . 2 3. Use and Negotiation in IKEv2 . . . . . . . . . . . . . . . . 3 3.1. Key Exchange Payload . . . . . . . . . . . . . . . . . . 3 3.2. Recipient Tests . . . . . . . . . . . . . . . . . . . . . 4 4. Security Considerations . . . . . . . . . . . . . . . . . . . 4 5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 4 6. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 5 7. References . . . . . . . . . . . . . . . . . . . . . . . . . 5 7.1. Normative References . . . . . . . . . . . . . . . . . . 5 7.2. Informative References . . . . . . . . . . . . . . . . . 5 Appendix A. Numerical Example for Curve25519 . . . . . . . . . . 6 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 7 1. Introduction The "Elliptic Curves for Security" document [RFC7748] describes two elliptic curves: Curve25519 and Curve448, as well as the X25519 and X448 functions for performing key agreement (Diffie-Hellman) operations with these curves. The curves and functions are designed for both performance and security. Elliptic curve Diffie-Hellman [RFC5903] has been specified for the Internet Key Exchange (IKEv2 - [RFC7296]) for almost ten years. That document specified the so-called NIST curves. The state of the art has advanced since then. More modern curves allow faster implementations while making it much easier to write constant-time implementations free from time-based side-channel attacks. This document defines two such curves for use in IKE. See [Curve25519] for details about the speed and security of the Curve25519 function. 1.1. Conventions Used in This Document The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in [RFC2119]. 2. Curve25519 & Curve448 All cryptographic computations are done using the X25519 and X448 functions defined in [RFC7748]. All related parameters (for example, the base point) and the encoding (in particular, pruning the least/ most significant bits and use of little-endian encoding) are inherited from [RFC7748]. Nir & Josefsson Expires March 3, 2017 [Page 2] Internet-Draft Curve25519 and Curve448 for IKEv2 August 2016 An ephemeral Diffie-Hellman key exchange using Curve25519 or Curve448 goes as follows: Each party picks a secret key d uniformly at random and computes the corresponding public key. "X" is used below to denote either X25519 or X448, and "G" is used to denote the corresponding base point: pub_mine = X(d, G) Parties exchange their public keys (see Section 3.1) and compute a shared secret: SHARED_SECRET = X(d, pub_peer). This shared secret is used directly as the value denoted g^ir in section 2.14 of RFC 7296. It is 32 octets when Curve25519 is used, and 56 octets when Curve448 is used. 3. Use and Negotiation in IKEv2 The use of Curve25519 and Curve448 in IKEv2 is negotiated using a Transform Type 4 (Diffie-Hellman group) in the SA payload of either an IKE_SA_INIT or a CREATE_CHILD_SA exchange. The value TBA1 is used for the group defined by Curve25519 and the value TBA2 is used for the group defined by Curve448. 3.1. Key Exchange Payload The diagram for the Key Exchange Payload from section 3.4 of RFC 7296 is copied below for convenience: 1 2 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | Next Payload |C| RESERVED | Payload Length | +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | Diffie-Hellman Group Num | RESERVED | +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ | | ~ Key Exchange Data ~ | | +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ o Payload Length - For Curve25519 the public key is 32 octets, so the Payload Length field will be 40, and for Curve448 the public key is 56 octets, so the Payload Length field will be 64. o The Diffie-Hellman Group Num is TBA1 for Curve25519, or TBA2 for Curve448. Nir & Josefsson Expires March 3, 2017 [Page 3] Internet-Draft Curve25519 and Curve448 for IKEv2 August 2016 o The Key Exchange Data is the 32 or 56 octets as described in section 6 of [RFC7748] 3.2. Recipient Tests This document matches the discussion in [RFC7748] related to receiving and accepting incompatible point formats. In particular, receiving entities MUST mask the most-significant bit in the final byte for X25519 (but not X448), and implementations MUST accept non- canonical values. See section 5 of [RFC7748] for further discussion. 4. Security Considerations Curve25519 and Curve448 are designed to facilitate the production of high-performance constant-time implementations. Implementors are encouraged to use a constant-time implementation of the functions. This point is of crucial importance if the implementation chooses to reuse its supposedly ephemeral key pair for many key exchanges, which some implementations do in order to improve performance. Curve25519 is intended for the ~128-bit security level, comparable to the 256-bit random ECP group (group 19) defined in RFC 5903, also known as NIST P-256 or secp256r1. Curve448 is intended for the ~224-bit security level. While the NIST curves are advertised as being chosen verifiably at random, there is no explanation for the seeds used to generate them. In contrast, the process used to pick these curves is fully documented and rigid enough so that independent verification has been done. This is widely seen as a security advantage, since it prevents the generating party from maliciously manipulating the parameters. Another family of curves available in IKE, generated in a fully verifiable way, is the Brainpool curves [RFC6954]. For example, brainpoolP256 (group 28) is expected to provide a level of security comparable to Curve25519 and NIST P-256. However, due to the use of pseudo-random prime, it is significantly slower than NIST P-256, which is itself slower than Curve25519. 5. IANA Considerations IANA is requested to assign two values from the IKEv2 "Transform Type 4 - Diffie-Hellman Group Transform IDs" registry, with names "Curve25519" and "Curve448" and this document as reference. The Recipient Tests field should also point to this document: Nir & Josefsson Expires March 3, 2017 [Page 4] Internet-Draft Curve25519 and Curve448 for IKEv2 August 2016 +--------+------------+---------------------+-----------+ | Number | Name | Recipient Tests | Reference | +--------+------------+---------------------+-----------+ | TBA1 | Curve25519 | RFCxxxx Section 3.2 | RFCxxxx | | TBA2 | Curve448 | RFCxxxx Section 3.2 | RFCxxxx | +--------+------------+---------------------+-----------+ Table 1: New Transform Type 4 Values 6. Acknowledgements Curve25519 was designed by D. J. Bernstein and the parameters for Curve448 ("Goldilocks") is by Mike Hamburg. The specification of algorithms, wire format and other considerations are in RFC 7748 by Adam Langley, Mike Hamburg, and Sean Turner. The example in Appendix A was calculated using the master version of OpenSSL, retrieved on August 4th, 2016. 7. References 7.1. Normative References [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997. [RFC7296] Kivinen, T., Kaufman, C., Hoffman, P., Nir, Y., and P. Eronen, "Internet Key Exchange Protocol Version 2 (IKEv2)", RFC 7296, October 2014. [RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves for Security", RFC 7748, January 2016. 7.2. Informative References [Curve25519] Bernstein, J., "Curve25519: New Diffie-Hellman Speed Records", LNCS 3958, February 2006, . [RFC5903] Fu, D. and J. Solinas, "Elliptic Curve Groups modulo a Prime (ECP Groups) for IKE and IKEv2", RFC 5903, June 2010. [RFC6954] Merkle, J. and M. Lochter, "Using the Elliptic Curve Cryptography (ECC) Brainpool Curves for the Internet Key Exchange Protocol Version 2 (IKEv2)", RFC 6954, July 2013. Nir & Josefsson Expires March 3, 2017 [Page 5] Internet-Draft Curve25519 and Curve448 for IKEv2 August 2016 Appendix A. Numerical Example for Curve25519 Suppose we have both the initiator and the responder generating private keys by generating 32 random octets. As usual in IKEv2 and its extension, we will denote Initiator values with the suffix _i and responder values with the suffix _r: random_i = 75 1f b4 30 86 55 b4 76 b6 78 9b 73 25 f9 ea 8c dd d1 6a 58 53 3f f6 d9 e6 00 09 46 4a 5f 9d 94 random_r = 0a 54 64 52 53 29 0d 60 dd ad d0 e0 30 ba cd 9e 55 01 ef dc 22 07 55 a1 e9 78 f1 b8 39 a0 56 88 These numbers need to be fixed by unsetting some bits as described in section 5 of RFC 7748. This affects only the first and last octets of each value: fixed_i = 70 1f b4 30 86 55 b4 76 b6 78 9b 73 25 f9 ea 8c dd d1 6a 58 53 3f f6 d9 e6 00 09 46 4a 5f 9d 54 fixed_r = 08 54 64 52 53 29 0d 60 dd ad d0 e0 30 ba cd 9e 55 01 ef dc 22 07 55 a1 e9 78 f1 b8 39 a0 56 48 The actual private keys are considered to be encoded in little-endian format: d_i = 549D5F4A460900E6D9F63F53586AD1DD8CEAF925739B78B676B4558630B41F70 d_r = 4856A039B8F178E9A1550722DCEF01559ECDBA30E0D0ADDD600D295352645408 The public keys are generated from this using the formula in Section 2: pub_i = X25519(d_i, G) = 48 d5 dd d4 06 12 57 ba 16 6f a3 f9 bb db 74 f1 a4 e8 1c 08 93 84 fa 77 f7 90 70 9f 0d fb c7 66 pub_r = X25519(d_r, G) = 0b e7 c1 f5 aa d8 7d 7e 44 86 62 67 32 98 a4 43 47 8b 85 97 45 17 9e af 56 4c 79 c0 ef 6e ee 25 And this is the value of the Key Exchange Data field in the key exchange payload described in Section 3.1. The shared value is calculated as in Section 2: SHARED_SECRET = X25519(d_i, pub_r) = X25519(d_r, pub_i) = c7 49 50 60 7a 12 32 7f-32 04 d9 4b 68 25 bf b0 68 b7 f8 31 9a 9e 37 08-ed 3d 43 ce 81 30 c9 50 Nir & Josefsson Expires March 3, 2017 [Page 6] Internet-Draft Curve25519 and Curve448 for IKEv2 August 2016 Authors' Addresses Yoav Nir Check Point Software Technologies Ltd. 5 Hasolelim st. Tel Aviv 6789735 Israel Email: ynir.ietf@gmail.com Simon Josefsson SJD AB Email: simon@josefsson.org Nir & Josefsson Expires March 3, 2017 [Page 7]