draft-ietf-ipsecme-safecurves-05.txt   rfc8031.txt 
Network Working Group Y. Nir Internet Engineering Task Force (IETF) Y. Nir
Internet-Draft Check Point Request for Comments: 8031 Check Point
Intended status: Standards Track S. Josefsson Category: Standards Track S. Josefsson
Expires: April 14, 2017 SJD ISSN: 2070-1721 SJD
October 11, 2016 December 2016
Curve25519 and Curve448 for IKEv2 Key Agreement Curve25519 and Curve448 for the
draft-ietf-ipsecme-safecurves-05 Internet Key Exchange Protocol Version 2 (IKEv2) Key Agreement
Abstract Abstract
This document describes the use of Curve25519 and Curve448 for This document describes the use of Curve25519 and Curve448 for
ephemeral key exchange in the Internet Key Exchange (IKEv2) protocol. ephemeral key exchange in the Internet Key Exchange Protocol Version
2 (IKEv2).
Status of This Memo Status of This Memo
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provisions of BCP 78 and BCP 79.
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Table of Contents Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. Conventions Used in This Document . . . . . . . . . . . . 2 1.1. Conventions Used in This Document . . . . . . . . . . . . 2
2. Curve25519 & Curve448 . . . . . . . . . . . . . . . . . . . . 2 2. Curve25519 and Curve448 . . . . . . . . . . . . . . . . . . . 3
3. Use and Negotiation in IKEv2 . . . . . . . . . . . . . . . . 3 3. Use and Negotiation in IKEv2 . . . . . . . . . . . . . . . . 3
3.1. Key Exchange Payload . . . . . . . . . . . . . . . . . . 3 3.1. Key Exchange Payload . . . . . . . . . . . . . . . . . . 4
3.2. Recipient Tests . . . . . . . . . . . . . . . . . . . . . 4 3.2. Recipient Tests . . . . . . . . . . . . . . . . . . . . . 4
4. Security Considerations . . . . . . . . . . . . . . . . . . . 4 4. Security Considerations . . . . . . . . . . . . . . . . . . . 4
5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 4 5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 5
6. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 5 6. References . . . . . . . . . . . . . . . . . . . . . . . . . 5
7. References . . . . . . . . . . . . . . . . . . . . . . . . . 5 6.1. Normative References . . . . . . . . . . . . . . . . . . 5
7.1. Normative References . . . . . . . . . . . . . . . . . . 5 6.2. Informative References . . . . . . . . . . . . . . . . . 6
7.2. Informative References . . . . . . . . . . . . . . . . . 5 Appendix A. Numerical Example for Curve25519 . . . . . . . . . . 7
Appendix A. Numerical Example for Curve25519 . . . . . . . . . . 6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 8
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 7 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 8
1. Introduction 1. Introduction
The "Elliptic Curves for Security" document [RFC7748] describes two The "Elliptic Curves for Security" document [RFC7748] describes two
elliptic curves: Curve25519 and Curve448, as well as the X25519 and elliptic curves, Curve25519 and Curve448, as well as the X25519 and
X448 functions for performing key agreement using Diffie-Hellman X448 functions for performing key agreement using Diffie-Hellman
operations with these curves. The curves and functions are designed operations with these curves. The curves and functions are designed
for both performance and security. for both performance and security.
Elliptic curve Diffie-Hellman [RFC5903] has been specified for the Elliptic curve Diffie-Hellman [RFC5903] has been specified for the
Internet Key Exchange (IKEv2 - [RFC7296]) for almost ten years. RFC Internet Key Exchange Protocol Version 2 (IKEv2) [RFC7296] for almost
5903 and its predecessor specified the so-called NIST curves. The ten years. RFC 5903 and its predecessor specified the so-called NIST
state of the art has advanced since then. More modern curves allow curves. The state of the art has advanced since then. More modern
faster implementations while making it much easier to write constant- curves allow faster implementations while making it much easier to
time implementations resilient to time-based side-channel attacks. write constant-time implementations that are resilient to time-based
This document defines two such curves for use in IKE. See side-channel attacks. This document defines two such curves for use
[Curve25519] for details about the speed and security of the in IKEv2. See [Curve25519] for details about the speed and security
Curve25519 function. of the Curve25519 function.
1.1. Conventions Used in This Document 1.1. Conventions Used in This Document
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in [RFC2119]. document are to be interpreted as described in [RFC2119].
2. Curve25519 & Curve448 2. Curve25519 and Curve448
Implementations of Curve25519 and Curve448 in IKEv2 SHALL follow the Implementations of Curve25519 and Curve448 in IKEv2 SHALL follow the
steps described in this section. All cryptographic computations are steps described in this section. All cryptographic computations are
done using the X25519 and X448 functions defined in [RFC7748]. All done using the X25519 and X448 functions defined in [RFC7748]. All
related parameters (for example, the base point) and the encoding (in related parameters (for example, the base point) and the encoding (in
particular, pruning the least/most significant bits and use of particular, pruning the least/most significant bits and using little-
little-endian encoding) are compliant with [RFC7748]. endian encoding) are compliant with [RFC7748].
An ephemeral Diffie-Hellman key exchange using Curve25519 or Curve448 An ephemeral Diffie-Hellman key exchange using Curve25519 or Curve448
is performed as follows: Each party picks a secret key d uniformly at is performed as follows: each party picks a secret key d uniformly at
random and computes the corresponding public key. "X" is used below random and computes the corresponding public key. "X" is used below
to denote either X25519 or X448, and "G" is used to denote the to denote either X25519 or X448, and "G" is used to denote the
corresponding base point: corresponding base point:
pub_mine = X(d, G) pub_mine = X(d, G)
Parties exchange their public keys (see Section 3.1) and compute a Parties exchange their public keys (see Section 3.1) and compute a
shared secret: shared secret:
SHARED_SECRET = X(d, pub_peer). SHARED_SECRET = X(d, pub_peer)
This shared secret is used directly as the value denoted g^ir in 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, Section 2.14 of RFC 7296. It is 32 octets when Curve25519 is used
and 56 octets when Curve448 is used. and 56 octets when Curve448 is used.
3. Use and Negotiation in IKEv2 3. Use and Negotiation in IKEv2
The use of Curve25519 and Curve448 in IKEv2 is negotiated using a The use of Curve25519 and Curve448 in IKEv2 is negotiated using a
Transform Type 4 (Diffie-Hellman group) in the SA payload of either Transform Type 4 (Diffie-Hellman group) in the Security Association
an IKE_SA_INIT or a CREATE_CHILD_SA exchange. The value TBA1 is used (SA) payload of either an IKE_SA_INIT or a CREATE_CHILD_SA exchange.
for the group defined by Curve25519 and the value TBA2 is used for The value 31 is used for the group defined by Curve25519 and the
the group defined by Curve448. value 32 is used for the group defined by Curve448.
3.1. Key Exchange Payload 3.1. Key Exchange Payload
The diagram for the Key Exchange Payload from section 3.4 of RFC 7296 The diagram for the Key Exchange payload from Section 3.4 of RFC 7296
is copied below for convenience: is copied below for convenience:
1 2 3 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 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 | | Next Payload |C| RESERVED | Payload Length |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Diffie-Hellman Group Num | RESERVED | | Diffie-Hellman Group Num | RESERVED |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| | | |
~ Key Exchange Data ~ ~ Key Exchange Data ~
| | | |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
o Payload Length - For Curve25519 the public key is 32 octets, so o Payload Length - For Curve25519, the public key is 32 octets, so
the Payload Length field will be 40, and for Curve448 the public the Payload Length field will be 40. For Curve448, the public key
key is 56 octets, so the Payload Length field will be 64. is 56 octets, so the Payload Length field will be 64.
o The Diffie-Hellman Group Num is TBA1 for Curve25519, or TBA2 for o The Diffie-Hellman Group Num is 31 for Curve25519 or 32 for
Curve448. Curve448.
o The Key Exchange Data is the 32 or 56 octets as described in o The Key Exchange Data is the 32 or 56 octets as described in
section 6 of [RFC7748] Section 6 of [RFC7748].
3.2. Recipient Tests 3.2. Recipient Tests
Receiving and handling of incompatible point formats MUST follow the Receiving and handling of incompatible point formats MUST follow the
considerations described in section 5 of [RFC7748]. In particular, considerations described in Section 5 of [RFC7748]. In particular,
receiving entities MUST mask the most-significant bit in the final receiving entities MUST mask the most-significant bit in the final
byte for X25519 (but not X448), and implementations MUST accept non- byte for X25519 (but not X448), and implementations MUST accept non-
canonical values. canonical values.
4. Security Considerations 4. Security Considerations
Curve25519 and Curve448 are designed to facilitate the production of Curve25519 and Curve448 are designed to facilitate the production of
high-performance constant-time implementations. Implementors are high-performance constant-time implementations. Implementors are
encouraged to use a constant-time implementation of the functions. encouraged to use a constant-time implementation of the functions.
This point is of crucial importance especially if the implementation This point is of crucial importance, especially if the implementation
chooses to reuse its ephemeral key pair in many key exchanges for chooses to reuse its ephemeral key pair in many key exchanges for
performance reasons. performance reasons.
Curve25519 is intended for the ~128-bit security level, comparable to Curve25519 is intended for the ~128-bit security level, comparable to
the 256-bit random ECP group (group 19) defined in RFC 5903, also the 256-bit random ECP Groups (group 19) defined in RFC 5903, also
known as NIST P-256 or secp256r1. Curve448 is intended for the known as NIST P-256 or secp256r1. Curve448 is intended for the
~224-bit security level. ~224-bit security level.
While the NIST curves are advertised as being chosen verifiably at While the NIST curves are advertised as being chosen verifiably at
random, there is no explanation for the seeds used to generate them. random, there is no explanation for the seeds used to generate them.
In contrast, the process used to pick Curve25519 and Curve448 is In contrast, the process used to pick Curve25519 and Curve448 is
fully documented and rigid enough so that independent verification fully documented and rigid enough so that independent verification
can and has been done. This is widely seen as a security advantage, can and has been done. This is widely seen as a security advantage
since it prevents the generating party from maliciously manipulating because it prevents the generating party from maliciously
the parameters. manipulating the parameters.
Another family of curves available in IKE that were generated in a Another family of curves available in IKE that were generated in a
fully verifiable way, is the Brainpool curves [RFC6954]. For fully verifiable way is the Brainpool curves [RFC6954]. For example,
example, brainpoolP256 (group 28) is expected to provide a level of brainpoolP256 (group 28) is expected to provide a level of security
security comparable to Curve25519 and NIST P-256. However, due to comparable to Curve25519 and NIST P-256. However, due to the use of
the use of pseudo-random prime, it is significantly slower than NIST pseudorandom prime, it is significantly slower than NIST P-256, which
P-256, which is itself slower than Curve25519. is itself slower than Curve25519.
5. IANA Considerations 5. IANA Considerations
IANA is requested to assign two values from the IKEv2 "Transform Type IANA has assigned two values for the names "Curve25519" and
4 - Diffie-Hellman Group Transform IDs" registry, with names "Curve448" in the IKEv2 "Transform Type 4 - Diffie-Hellman Group
"Curve25519" and "Curve448" and this document as reference. The Transform IDs" and has listed this document as the reference. The
Recipient Tests field should also point to this document: Recipient Tests field should also point to this document:
+--------+------------+---------------------+-----------+ +--------+------------+-----------------------+-----------+
| Number | Name | Recipient Tests | Reference | | Number | Name | Recipient Tests | Reference |
+--------+------------+---------------------+-----------+ +--------+------------+-----------------------+-----------+
| TBA1 | Curve25519 | RFCxxxx Section 3.2 | RFCxxxx | | 31 | Curve25519 | RFC 8031, Section 3.2 | RFC 8031 |
| TBA2 | Curve448 | RFCxxxx Section 3.2 | RFCxxxx | | 32 | Curve448 | RFC 8031, Section 3.2 | RFC 8031 |
+--------+------------+---------------------+-----------+ +--------+------------+-----------------------+-----------+
Table 1: New Transform Type 4 Values Table 1: New Transform Type 4 Values
6. Acknowledgements 6. References
Curve25519 was designed by D. J. Bernstein and the parameters for
Curve448 ("Goldilocks") were defined by Mike Hamburg. The
specification of algorithms, wire format and other considerations are
documented 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 6.1. Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997. Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<http://www.rfc-editor.org/info/rfc2119>.
[RFC7296] Kivinen, T., Kaufman, C., Hoffman, P., Nir, Y., and P. [RFC7296] Kaufman, C., Hoffman, P., Nir, Y., Eronen, P., and T.
Eronen, "Internet Key Exchange Protocol Version 2 Kivinen, "Internet Key Exchange Protocol Version 2
(IKEv2)", RFC 7296, October 2014. (IKEv2)", STD 79, RFC 7296, DOI 10.17487/RFC7296, October
2014, <http://www.rfc-editor.org/info/rfc7296>.
[RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves [RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
for Security", RFC 7748, January 2016. for Security", RFC 7748, DOI 10.17487/RFC7748, January
2016, <http://www.rfc-editor.org/info/rfc7748>.
7.2. Informative References 6.2. Informative References
[Curve25519] [Curve25519]
Bernstein, J., "Curve25519: New Diffie-Hellman Speed Bernstein, J., "Curve25519: New Diffie-Hellman Speed
Records", LNCS 3958, February 2006, Records", Public Key Cryptography - PKC 2006, Lecture
Notes in Computer Science (LNCS), Vol. 3958, pp. 207-228,
DOI 10.1007/11745853_14, February 2006,
<http://dx.doi.org/10.1007/11745853_14>. <http://dx.doi.org/10.1007/11745853_14>.
[RFC5903] Fu, D. and J. Solinas, "Elliptic Curve Groups modulo a [RFC5903] Fu, D. and J. Solinas, "Elliptic Curve Groups modulo a
Prime (ECP Groups) for IKE and IKEv2", RFC 5903, June Prime (ECP Groups) for IKE and IKEv2", RFC 5903,
2010. DOI 10.17487/RFC5903, June 2010,
<http://www.rfc-editor.org/info/rfc5903>.
[RFC6954] Merkle, J. and M. Lochter, "Using the Elliptic Curve [RFC6954] Merkle, J. and M. Lochter, "Using the Elliptic Curve
Cryptography (ECC) Brainpool Curves for the Internet Key Cryptography (ECC) Brainpool Curves for the Internet Key
Exchange Protocol Version 2 (IKEv2)", RFC 6954, July 2013. Exchange Protocol Version 2 (IKEv2)", RFC 6954,
DOI 10.17487/RFC6954, July 2013,
<http://www.rfc-editor.org/info/rfc6954>.
Appendix A. Numerical Example for Curve25519 Appendix A. Numerical Example for Curve25519
Suppose we have both the initiator and the responder generating Suppose we have both the initiator and the responder generating
private keys by generating 32 random octets. As usual in IKEv2 and private keys by generating 32 random octets. As usual in IKEv2 and
its extension, we will denote Initiator values with the suffix _i and its extension, we will denote Initiator values with the suffix _i and
responder values with the suffix _r: responder values with the suffix _r:
random_i = 75 1f b4 30 86 55 b4 76 b6 78 9b 73 25 f9 ea 8c 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 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 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 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 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 Section 5 of RFC 7748. This affects only the first and last octets
of each value: of each value:
fixed_i = 70 1f b4 30 86 55 b4 76 b6 78 9b 73 25 f9 ea 8c 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 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 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 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 The actual private keys are considered to be encoded in little-endian
format: format:
skipping to change at page 6, line 46 skipping to change at page 7, line 46
Section 2: Section 2:
pub_i = X25519(d_i, G) = pub_i = X25519(d_i, G) =
48 d5 dd d4 06 12 57 ba 16 6f a3 f9 bb db 74 f1 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 a4 e8 1c 08 93 84 fa 77 f7 90 70 9f 0d fb c7 66
pub_r = X25519(d_r, G) = pub_r = X25519(d_r, G) =
0b e7 c1 f5 aa d8 7d 7e 44 86 62 67 32 98 a4 43 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 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 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 Exchange payload described in Section 3.1. The shared value is
calculated as in Section 2: calculated as in Section 2:
SHARED_SECRET = X25519(d_i, pub_r) = X25519(d_r, pub_i) = 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 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 68 b7 f8 31 9a 9e 37 08-ed 3d 43 ce 81 30 c9 50
Acknowledgements
Curve25519 was designed by D. J. Bernstein and the parameters for
Curve448 ("Goldilocks") were defined by Mike Hamburg. The
specification of algorithms, wire format, and other considerations
are documented 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.
Authors' Addresses Authors' Addresses
Yoav Nir Yoav Nir
Check Point Software Technologies Ltd. Check Point Software Technologies Ltd.
5 Hasolelim st. 5 Hasolelim st.
Tel Aviv 6789735 Tel Aviv 6789735
Israel Israel
Email: ynir.ietf@gmail.com Email: ynir.ietf@gmail.com
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