Network Working Group J. Merkle
Internet-Draft secunet Security Networks
Updates: 4492 (if approved) M. Lochter
Intended status: Informational Bundesamt fuer Sicherheit in der
Expires: May 9, 2013 Informationstechnik (BSI)
November 5, 2012
ECC Brainpool Curves for Transport Layer Security (TLS)
draft-merkle-tls-brainpool-00
Abstract
This document specifies the use of several ECC Brainpool elliptic
curves for authentication and key exchange in the Transport Layer
Security (TLS) protocol.
Status of This Memo
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This Internet-Draft will expire on May 9, 2013.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Values to be Used in the Supported Elliptic Curve Extension . 4
3. Security Considerations . . . . . . . . . . . . . . . . . . . 5
4. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 6
5. Intellectual Property Rights . . . . . . . . . . . . . . . . . 7
6. References . . . . . . . . . . . . . . . . . . . . . . . . . . 8
6.1. Normative References . . . . . . . . . . . . . . . . . . . 8
6.2. Informative References . . . . . . . . . . . . . . . . . . 8
Appendix A. Test Vectors . . . . . . . . . . . . . . . . . . . . 10
A.1. 256 Bit Curve . . . . . . . . . . . . . . . . . . . . . . 10
A.2. 384 Bit Curve . . . . . . . . . . . . . . . . . . . . . . 11
A.3. 512 Bit Curve . . . . . . . . . . . . . . . . . . . . . . 11
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1. Introduction
In [RFC5639], a new set of elliptic curve groups over finite prime
fields for use in cryptographic applications was specified. These
groups, denoted as ECC Brainpool curves, were generated in a
verifiably pseudo-random way and comply with the security
requirements of relevant standards from ISO [ISO1] [ISO2], ANSI
[ANSI1], NIST [FIPS], and SecG [SEC2].
Usage of elliptic curves for authentication and key agreement in TLS
1.1 and TLS 2.0 is defined in [RFC4492]. While the ASN.1 object
identifiers defined in [RFC5639] already allow usage of the ECC
Brainpool curves for TLS (client or server) authentication through
reference in X.509 certificates according to [RFC3279], their
negotiation for key exchange according to [RFC4492] requires the
definition and assignment of additional NamedCurve IDs. This
document specifies such values for three curves from [RFC5639].
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2. Values to be Used in the Supported Elliptic Curve Extension
According to [RFC4492], the Supported Elliptic Curve Extension allows
the negotiation of elliptic curve groups during a handshake starting
a new TLS session. A client that proposes ECC cipher suites in its
ClientHello message SHOULD include this extension to indicate the
elliptic curves it supports through NamedCurve IDs, and a server that
receives a ClientHello containing this extension MUST use the
client's enumerated capabilities to guide its selection of an
appropriate cipher suite. Furthermore, the server SHOULD use a
NamedCurve ID, if applicable, to specify the elliptic curve
corresponding to its ephemeral ECDH public key.
The values of NamedCurve, by which the elliptic curves are
identified, are governed by the EC Named Curve Registry of IANA
[IANA-TLS]. In Table 1, new values for NamedCurve for three of the
ECC Brainpool curves defined in [RFC5639] are specified. All three
curves are suitable for usage in DTLS [RFC6347].
+-----------------+-------+
| Curve | Value |
+-----------------+-------+
| brainpoolP256r1 | TBD1 |
| | |
| brainpoolP384r1 | TBD2 |
| | |
| brainpoolP512r1 | TBD3 |
+-----------------+-------+
Table 1
Test vectors for a Diffie-Hellman key exchange using these ECC
Brainpool curves are provided in Appendix A
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3. Security Considerations
The security considerations of [RFC5246] apply accordingly.
The confidentiality, authenticity and integrity of the TLS
communication is limited by the weakest cryptographic primitive
applied. In order to achieve a maximum security level when using one
of the elliptic curves from Table 1 for authentication and / or key
exchange in TLS, the key derivation function, the algorithms and key
lengths of symmetric encryption and message authentication as well as
the algorithm, bit length and hash function used for signature
generation should be chosen according to the recommendations of
[NIST800-57] and [RFC5639]. Furthermore, the private Diffie-Hellman
keys should be selected with the same bit length as the order of the
group generated by the base point G and with approximately maximum
entropy.
Implementations of elliptic curve cryptography for TLS may be
susceptible to side-channel attacks. Particular care should be taken
for implementations that internally transform curve points to points
on the corresponding "twisted curve", using the map (x',y') = (x*Z^2,
y*Z^3) with the coefficient Z specified for that curve in [RFC5639],
in order to take advantage of an an efficient arithmetic based on the
twisted curve's special parameters (A = -3): although the twisted
curve itself offers the same level of security as the corresponding
random curve (through mathematical equivalence), an arithmetic based
on small curve parameters may be harder to protect against side-
channel attacks. General guidance on resistence of elliptic curve
cryptography implementations against side-channel-attacks is given in
[BSI1] and [HMV].
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4. IANA Considerations
Before this document can become an RFC, IANA is required to assign
numbers for the elliptic curves specified in Table 1 to the
NamedCurve name space in its Transport Layer Security (TLS)
Parameters registry [IANA-TLS]. For all these elliptic curves,
suitability with DTLS shall be indicated in the registry.
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5. Intellectual Property Rights
Although, the authors have no knowledge about any intellectual
property rights which cover the general usage of the ECP groups
defined herein, implementations based on these domain parameters may
require use of inventions covered by patent rights. In particular,
techniques for an efficient arithmetic exploiting the special
parameters of the twisted curves (see Section 3) may be covered by
patents.
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6. References
6.1. Normative References
[IANA-TLS] Internet Assigned Numbers Authority, "Transport Layer
Security (TLS) Parameters", .
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC4492] Blake-Wilson, S., Bolyard, N., Gupta, V., Hawk, C., and
B. Moeller, "Elliptic Curve Cryptography (ECC) Cipher
Suites for Transport Layer Security (TLS)", RFC 4492,
May 2006.
[RFC5246] Dierks, T. and E. Rescorla, "The Transport Layer
Security (TLS) Protocol Version 1.2", RFC 5246,
August 2008.
[RFC5639] Lochter, M. and J. Merkle, "Elliptic Curve Cryptography
(ECC) Brainpool Standard Curves and Curve Generation",
RFC 5639, March 2010.
[RFC6347] Rescorla, E. and N. Modadugu, "Datagram Transport Layer
Security Version 1.2", RFC 6347, January 2012.
6.2. Informative References
[ANSI1] American National Standards Institute, "Public Key
Cryptography For The Financial Services Industry: The
Elliptic Curve Digital Signature Algorithm (ECDSA)",
ANSI X9.62, 2005.
[BSI1] Bundesamt fuer Sicherheit in der Informationstechnik,
"Minimum Requirements for Evaluating Side-Channel
Attack Resistance of Elliptic Curve Implementations",
July 2011.
[FIPS] National Institute of Standards and Technology,
"Digital Signature Standard (DSS)", FIPS PUB 186-2,
December 1998.
[HMV] Hankerson, D., Menezes, A., and S. Vanstone, "Guide to
Elliptic Curve Cryptography", Springer Verlag, 2004.
[ISO1] International Organization for Standardization,
"Information Technology - Security Techniques - Digital
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Signatures with Appendix - Part 3: Discrete Logarithm
Based Mechanisms", ISO/IEC 14888-3, 2006.
[ISO2] International Organization for Standardization,
"Information Technology - Security Techniques -
Cryptographic Techniques Based on Elliptic Curves -
Part 2: Digital signatures", ISO/IEC 15946-2, 2002.
[NIST800-57] National Institute of Standards and Technology,
"Recommendation for Key Management - Part 1: General
(Revised)", NIST Special Publication 800-57,
March 2007.
[RFC3279] Bassham, L., Polk, W., and R. Housley, "Algorithms and
Identifiers for the Internet X.509 Public Key
Infrastructure Certificate and Certificate Revocation
List (CRL) Profile", RFC 3279, April 2002.
[RFC6090] McGrew, D., Igoe, K., and M. Salter, "Fundamental
Elliptic Curve Cryptography Algorithms", RFC 6090,
February 2011.
[SEC1] Certicom Research, "Elliptic Curve Cryptography",
Standards for Efficient Cryptography (SEC) 1,
September 2000.
[SEC2] Certicom Research, "Recommended Elliptic Curve Domain
Parameters", Standards for Efficient Cryptography
(SEC) 2, September 2000.
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Appendix A. Test Vectors
This section provides some test vectors for example Diffie-Hellman
key exchanges using each of the curves defined in Section 2 . In all
of the following sections the following notation is used:
d_A: the secret key of party A
x_qA: the x-coordinate of the public key of party A
y_qA: the y-coordinate of the public key of party A
d_B: the secret key of party B
x_qB: the x-coordinate of the public key of party B
y_qB: the y-coordinate of the public key of party B
x_Z: the x-coordinate of the shared secret that results from
completion of the Diffie-Hellman computation, i.e. the hex
representation of the pre-master secret
y_Z: the y-coordinate of the shared secret that results from
completion of the Diffie-Hellman computation
The field elements x_qA, y_qA, x_qB, y_qB, x_Z, y_Z are represented
as hexadecimal values using the FieldElement-to-OctetString
conversion method specified in [SEC1].
A.1. 256 Bit Curve
Curve brainpoolP256r1
dA =
81DB1EE100150FF2EA338D708271BE38300CB54241D79950F77B063039804F1D
x_qA =
44106E913F92BC02A1705D9953A8414DB95E1AAA49E81D9E85F929A8E3100BE5
y_qA =
8AB4846F11CACCB73CE49CBDD120F5A900A69FD32C272223F789EF10EB089BDC
dB =
55E40BC41E37E3E2AD25C3C6654511FFA8474A91A0032087593852D3E7D76BD3
x_qB =
8D2D688C6CF93E1160AD04CC4429117DC2C41825E1E9FCA0ADDD34E6F1B39F7B
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y_qB =
990C57520812BE512641E47034832106BC7D3E8DD0E4C7F1136D7006547CEC6A
x_Z =
89AFC39D41D3B327814B80940B042590F96556EC91E6AE7939BCE31F3A18BF2B
y_Z =
49C27868F4ECA2179BFD7D59B1E3BF34C1DBDE61AE12931648F43E59632504DE
A.2. 384 Bit Curve
Curve brainpoolP384r1
dA = 1E20F5E048A5886F1F157C74E91BDE2B98C8B52D58E5003D57053FC4B0BD6
5D6F15EB5D1EE1610DF870795143627D042
x_qA = 68B665DD91C195800650CDD363C625F4E742E8134667B767B1B47679358
8F885AB698C852D4A6E77A252D6380FCAF068
y_qA = 55BC91A39C9EC01DEE36017B7D673A931236D2F1F5C83942D049E3FA206
07493E0D038FF2FD30C2AB67D15C85F7FAA59
dB = 032640BC6003C59260F7250C3DB58CE647F98E1260ACCE4ACDA3DD869F74E
01F8BA5E0324309DB6A9831497ABAC96670
x_qB = 4D44326F269A597A5B58BBA565DA5556ED7FD9A8A9EB76C25F46DB69D19
DC8CE6AD18E404B15738B2086DF37E71D1EB4
y_qB = 62D692136DE56CBE93BF5FA3188EF58BC8A3A0EC6C1E151A21038A42E91
85329B5B275903D192F8D4E1F32FE9CC78C48
x_Z = 0BD9D3A7EA0B3D519D09D8E48D0785FB744A6B355E6304BC51C229FBBCE2
39BBADF6403715C35D4FB2A5444F575D4F42
y_Z = 0DF213417EBE4D8E40A5F76F66C56470C489A3478D146DECF6DF0D94BAE9
E598157290F8756066975F1DB34B2324B7BD
A.3. 512 Bit Curve
Curve brainpoolP512r1
dA = 16302FF0DBBB5A8D733DAB7141C1B45ACBC8715939677F6A56850A38BD87B
D59B09E80279609FF333EB9D4C061231FB26F92EEB04982A5F1D1764CAD5766542
2
x_qA = 0A420517E406AAC0ACDCE90FCD71487718D3B953EFD7FBEC5F7F27E28C6
149999397E91E029E06457DB2D3E640668B392C2A7E737A7F0BF04436D11640FD0
9FD
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y_qA = 72E6882E8DB28AAD36237CD25D580DB23783961C8DC52DFA2EC138AD472
A0FCEF3887CF62B623B2A87DE5C588301EA3E5FC269B373B60724F5E82A6AD147F
DE7
dB = 230E18E1BCC88A362FA54E4EA3902009292F7F8033624FD471B5D8ACE49D1
2CFABBC19963DAB8E2F1EBA00BFFB29E4D72D13F2224562F405CB80503666B2542
9
x_qB = 9D45F66DE5D67E2E6DB6E93A59CE0BB48106097FF78A081DE781CDB31FC
E8CCBAAEA8DD4320C4119F1E9CD437A2EAB3731FA9668AB268D871DEDA55A54731
99F
y_qB = 2FDC313095BCDD5FB3A91636F07A959C8E86B5636A1E930E8396049CB48
1961D365CC11453A06C719835475B12CB52FC3C383BCE35E27EF194512B7187628
5FA
x_Z = A7927098655F1F9976FA50A9D566865DC530331846381C87256BAF322624
4B76D36403C024D7BBF0AA0803EAFF405D3D24F11A9B5C0BEF679FE1454B21C4CD
1F
y_Z = 7DB71C3DEF63212841C463E881BDCF055523BD368240E6C3143BD8DEF8B3
B3223B95E0F53082FF5E412F4222537A43DF1C6D25729DDB51620A832BE6A26680
A2
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Authors' Addresses
Johannes Merkle
secunet Security Networks
Mergenthaler Allee 77
65760 Eschborn
Germany
Phone: +49 201 5454 3091
EMail: johannes.merkle@secunet.com
Manfred Lochter
Bundesamt fuer Sicherheit in der Informationstechnik (BSI)
Postfach 200363
53133 Bonn
Germany
Phone: +49 228 9582 5643
EMail: manfred.lochter@bsi.bund.de
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