< draft-nir-ipsecme-curve25519-00.txt   draft-nir-ipsecme-curve25519-01.txt >
Network Working Group Y. Nir Network Working Group Y. Nir
Internet-Draft Check Point Internet-Draft Check Point
Intended status: Standards Track S. Josefsson Intended status: Standards Track S. Josefsson
Expires: December 13, 2015 SJD Expires: January 8, 2016 SJD
June 11, 2015 July 7, 2015
Using Curve25519 for IKEv2 Key Agreement New Safe Curves for IKEv2 Key Agreement
draft-nir-ipsecme-curve25519-00 draft-nir-ipsecme-curve25519-01
Abstract Abstract
This document describes the use of Curve25519 for ephemeral key This document describes the use of Curve25519 and Curve448
exchange in the Internet Key Exchange (IKEv2) protocol. ("Goldilocks") for ephemeral key exchange in the Internet Key
Exchange (IKEv2) protocol.
Status of This Memo Status of This Memo
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provisions of BCP 78 and BCP 79. provisions of BCP 78 and BCP 79.
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Copyright Notice Copyright Notice
Copyright (c) 2015 IETF Trust and the persons identified as the Copyright (c) 2015 IETF Trust and the persons identified as the
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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 . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. Curve25519 & 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 . . . . . . . . . . . . . . . . . . . 5 4. Security Considerations . . . . . . . . . . . . . . . . . . . 5
5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 5 5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 5
6. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 5 6. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 5
7. References . . . . . . . . . . . . . . . . . . . . . . . . . 5 7. References . . . . . . . . . . . . . . . . . . . . . . . . . 6
7.1. Normative References . . . . . . . . . . . . . . . . . . 6 7.1. Normative References . . . . . . . . . . . . . . . . . . 6
7.2. Informative References . . . . . . . . . . . . . . . . . 6 7.2. Informative References . . . . . . . . . . . . . . . . . 6
Appendix A. The curve25519 function . . . . . . . . . . . . . . 6 Appendix A. The curve25519 function . . . . . . . . . . . . . . 6
A.1. Formulas . . . . . . . . . . . . . . . . . . . . . . . . 6 A.1. Formulas . . . . . . . . . . . . . . . . . . . . . . . . 7
A.1.1. Field Arithmetic . . . . . . . . . . . . . . . . . . 7 A.1.1. Field Arithmetic . . . . . . . . . . . . . . . . . . 7
A.1.2. Conversion to and from internal format . . . . . . . 7 A.1.2. Conversion to and from internal format . . . . . . . 7
A.1.3. Scalar Multiplication . . . . . . . . . . . . . . . . 7 A.1.3. Scalar Multiplication . . . . . . . . . . . . . . . . 8
A.1.4. Conclusion . . . . . . . . . . . . . . . . . . . . . 9 A.1.4. Conclusion . . . . . . . . . . . . . . . . . . . . . 9
A.2. Test vectors . . . . . . . . . . . . . . . . . . . . . . 9 A.2. Test vectors . . . . . . . . . . . . . . . . . . . . . . 9
A.3. Side-channel considerations . . . . . . . . . . . . . . . 10 A.3. Side-channel considerations . . . . . . . . . . . . . . . 10
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 11 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 11
1. Introduction 1. Introduction
[CFRG-Curves] specifies a new elliptic curve function for use in [CFRG-Curves] specifies two new elliptic curve functions for use in
cryptographic applications. Curve25519 is a Diffie-Hellman function cryptographic applications. Curve25519 and Curve448 (also known as
designed with performance and security in mind. "Goldilocks") are Diffie-Hellman functions designed with performance
and security in mind.
Almost ten years ago [RFC4753] specified the first elliptic curve Almost ten years ago [RFC4753] specified the first elliptic curve
Diffie-Hellman groups for the Internet Key Exchange protocol (IKEv2 - Diffie-Hellman groups for the Internet Key Exchange protocol (IKEv2 -
[RFC7296]). These were the so-called NIST curves. The state of the [RFC7296]). These were the so-called NIST curves. The state of the
art has advanced since then. More modern curves allow faster art has advanced since then. More modern curves allow faster
implementations while making it much easier to write constant-time implementations while making it much easier to write constant-time
implementations free from side-channel attacks. This document implementations free from side-channel attacks. This document
defines such a curve for use in IKE. See [Curve25519] for details defines such a curve for use in IKE. See [Curve25519] for details
about the speed and security of this curve. about the speed and security 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 2. Curve25519 & Curve448
All cryptographic computations are done using the Curve25519 function All cryptographic computations are done using the Curve25519 and
defined in [CFRG-Curves]. In this document, this function is Curve448 functions defined in [CFRG-Curves]. In this document, these
considered a black box that takes for input a (secret key, public functions are considered black boxes that take for input a (secret
key) pair and outputs a public key. Public keys are defined as key, public key) pair and output a public key. Public keys for are
strings of 32 octets. Secret keys are defined as 255-bit numbers defined as strings of 32 octets. A common public key, denoted below
such that high-order bit (bit 254) is set, and the three lowest-order as G (or "base point" in the curves document) is shared by all users.
bits are unset. In addition, a common public key, denoted by G, is Since the functions only use the u-coordinate of the public key, only
shared by all users. the u coordinate of the base points is necessary. For Curve25519
Gu=9 ; for Curve448 Gu=5.
An ephemeral Diffie-Hellman key exchange using Curve25519 goes as For Curve25519 secret keys are defined as 255-bit numbers such that
follows: Each party picks a secret key d uniformly at random and the high-order bit (bit 254) is set, and the three lowest-order bits
computes the corresponding public key: are unset.
x_mine = Curve25519(d, G) For Curve448 secret keys are defined as 448-bit numbers such that the
high-order bit (bit 447) is set, and the two lowest-order bits are
unset.
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. "curve_function" is used
below to denote either Curve25519 or Curve448:
x_mine = curve_function(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 = Curve25519(d, x_peer). SHARED_SECRET = curve_function(d, x_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 always exactly 32 octets when section 2.14 of RFC 7296. It is always exactly 32 octets when these
Curve25519 is used. functions are used.
A complete description of the Curve25519 function, as well as a few A complete description of the Curve25519 function, as well as a few
implementation notes, are provided in Appendix A. implementation notes, are provided in Appendix A.
3. Use and Negotiation in IKEv2 3. Use and Negotiation in IKEv2
The use of Curve25519 in IKEv2 is negotiated using a Transform Type 4 The use of Curve25519 and Curve448 in IKEv2 is negotiated using a
(Diffie-Hellman group) in the SA payload of either an IKE_SA_INIT or Transform Type 4 (Diffie-Hellman group) in the SA payload of either
a CREATE_CHILD_SA exchange. an IKE_SA_INIT or a CREATE_CHILD_SA exchange.
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 - Since a Curve25519 public key is 32 octets, the o Payload Length - Since the public key is 32 octets, the Payload
Payload Length is always 40. Length field always contains 40.
o The Diffie-Hellman Group Num is xx for Curve25519 (TBA by IANA) o The Diffie-Hellman Group Num is xx for Curve25519, or yy for
Curve448 (both TBA by IANA).
o The Key Exchange Data is 32 octets encoded as an array of bytes in o The Key Exchange Data is 32 octets encoded as an array of bytes in
little-endian order as described in section 8 of [CFRG-Curves] little-endian order as described in section 8 of [CFRG-Curves]
3.2. Recipient Tests 3.2. Recipient Tests
This section describes the checks that a recipient of a public key This section describes the checks that a recipient of a public key
needs to perform. It is the equivalent of the tests described in needs to perform. It is the equivalent of the tests described in
[RFC6989] for other Diffie-Hellman groups. [RFC6989] for other Diffie-Hellman groups. We use "func" to denote
either Curve25519 or Curve448, as the tests are similar to both.
Curve25519 was designed in a way that the result of Curve25519(x, d) Both functions were designed in a way that the result of func(d, x)
will never reveal information about d, provided is was chosen as will never reveal information about d, provided it was chosen as
prescribed, for any value of x. prescribed, for any value of x.
Define legitimate values of x as the values that can be obtained as x Define legitimate values of x as the values that can be obtained as x
= Curve25519(G, d') for some d, and call the other values = func(d, G) for some d, and call the other values illegitimate. The
illegitimate. The definition of the Curve25519 function shows that definitions of the functions show that legitimate values all share
legitimate values all share the following property: the high-order the following property: the high-order bit of the last byte is not
bit of the last byte is not set. set.
Since there are some implementation of the Curve25519 function that Since there are some implementation of these functions that impose
impose this restriction on their input and others that don't, this restriction on their input and others that don't, IKEv2
implementations of Curve25519 in IKE SHOULD reject public keys when implementations SHOULD reject public keys when the high-order bit of
the high-order bit of the last byte is set (in other words, when the the last byte is set (in other words, when the value of the leftmost
value of the leftmost byte is greater than 0x7F) in order to prevent byte is greater than 0x7F) in order to prevent implementation
implementation fingerprinting. fingerprinting.
Other than this recommended check, implementations do not need to Other than this recommended check, implementations do not need to
ensure that the public keys they receive are legitimate: this is not ensure that the public keys they receive are legitimate: this is not
necessary for security with Curve25519. necessary for security.
4. Security Considerations 4. Security Considerations
Curve25519 is designed to facilitate the production of high- Curve25519 is designed to facilitate the production of high-
performance constant-time implementations of the Curve25519 function. performance constant-time implementations. Implementors are
Implementors are encouraged to use a constant-time implementation of encouraged to use a constant-time implementation of the Curve25519
the Curve25519 function. This point is of crucial importance if the function. This point is of crucial importance if the implementation
implementation chooses to reuse its supposedly ephemeral key pair for chooses to reuse its supposedly ephemeral key pair for many key
many key exchanges, which some implementations do in order to improve exchanges, which some implementations do in order to improve
performance. performance. The same is true for Curve448.
Curve25519 is believed to be at least as secure as the 256-bit random Curve25519 is believed to be at least as secure as the 256-bit random
ECP group (group 19) defined in RFC 4753, also known as NIST P-256. ECP group (group 19) defined in RFC 4753, also known as NIST P-256 or
secp256r1. Curve448 is believed to be more secure than the 384-bit
random ECP group (group 20), also known as NIST P-384 or secp384r1.
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 is fully documented In contrast, the process used to pick these curves is fully
and rigid enough so that independent verification has been done. documented and rigid enough so that independent verification has been
This is widely seen as a security advantage for Curve25519, since it done. This is widely seen as a security advantage for Curve25519,
prevents the generating party from maliciously manipulating the since it prevents the generating party from maliciously manipulating
parameters. the parameters.
Another family of curves available in IKE, generated in a fully Another family of curves available in IKE, generated in a fully
verifiable way, is the Brainpool curves [RFC6954]. Specifically, verifiable way, is the Brainpool curves [RFC6954]. Specifically,
brainpoolP256 (group 28) is expected to provide a level of security brainpoolP256 (group 28) is expected to provide a level of security
comparable to Curve25519 and NIST P-256. However, due to the use of comparable to Curve25519 and NIST P-256. However, due to the use of
pseudo-random prime, it is significantly slower than NIST P-256, pseudo-random prime, it is significantly slower than NIST P-256,
which is itself slower than Curve25519. which is itself slower than Curve25519.
5. IANA Considerations 5. IANA Considerations
IANA is requested to assign one value from the IKEv2 "Transform Type IANA is requested to assign two values from the IKEv2 "Transform Type
4 - Diffie-Hellman Group Transform IDs" registry, with name 4 - Diffie-Hellman Group Transform IDs" registry, with names
Curve25519, and this document as reference. The Recipient Tests "Curve25519" and "Curve448" and this document as reference. The
field should also point to this document. Recipient Tests field should also point to this document.
6. Acknowledgements 6. Acknowledgements
Curve25519 was designed by D. J. Bernstein and Tanja Lange. The Curve25519 was designed by D. J. Bernstein and Tanja Lange.
specification of wire format is by Sean Turner, Rich Salz, and Watson Curve448 ("Goldilocks") is by Mike Hamburg. The specification of
Ladd, with Adam Langley editing the current document. Much of the wire format is Sean Turner, Rich Salz, and Watson Ladd, with Adam
text in this document is copied from Simon's draft for the TLS Langley editing the current document. Much of the text in this
working group. document is copied from Simon's draft for the TLS working group.
7. References 7. References
7.1. Normative References 7.1. Normative References
[CFRG-Curves] [CFRG-Curves]
Langley, A., "Elliptic Curves for Security", draft-agl- Langley, A., Salz, R., and S. Turner, "Elliptic Curves for
cfrgcurve-00 (work in progress), January 2015. Security", draft-irtf-cfrg-curves-02 (work in progress),
March 2015.
[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, March 1997.
[RFC7296] Kivinen, T., Kaufman, C., Hoffman, P., Nir, Y., and P. [RFC7296] Kivinen, T., Kaufman, C., Hoffman, P., Nir, Y., and P.
Eronen, "Internet Key Exchange Protocol Version 2 Eronen, "Internet Key Exchange Protocol Version 2
(IKEv2)", RFC 7296, October 2014. (IKEv2)", RFC 7296, October 2014.
7.2. Informative References 7.2. Informative References
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