Elliptic Curve Cryptography (ECC) Brainpool Standard Curves and Curve Generation
RFC 5639
Document | Type | RFC - Informational (March 2010; Errata) | |
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Authors | Johannes Merkle , Manfred Lochter | ||
Last updated | 2020-01-21 | ||
Stream | ISE | ||
Formats | plain text html pdf htmlized with errata bibtex | ||
Stream | ISE state | (None) | |
Consensus Boilerplate | Unknown | ||
Document shepherd | No shepherd assigned | ||
IESG | IESG state | RFC 5639 (Informational) | |
Action Holders |
(None)
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Telechat date | |||
Responsible AD | Tim Polk | ||
Send notices to | rfc-ise@rfc-editor.org |
Independent Submission M. Lochter Request for Comments: 5639 BSI Category: Informational J. Merkle ISSN: 2070-1721 secunet Security Networks March 2010 Elliptic Curve Cryptography (ECC) Brainpool Standard Curves and Curve Generation Abstract This memo proposes several elliptic curve domain parameters over finite prime fields for use in cryptographic applications. The domain parameters are consistent with the relevant international standards, and can be used in X.509 certificates and certificate revocation lists (CRLs), for Internet Key Exchange (IKE), Transport Layer Security (TLS), XML signatures, and all applications or protocols based on the cryptographic message syntax (CMS). Status of This Memo This document is not an Internet Standards Track specification; it is published for informational purposes. This is a contribution to the RFC Series, independently of any other RFC stream. The RFC Editor has chosen to publish this document at its discretion and makes no statement about its value for implementation or deployment. Documents approved for publication by the RFC Editor are not a candidate for any level of Internet Standard; see Section 2 of RFC 5741. Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at http://www.rfc-editor.org/info/rfc5639. Copyright Notice Copyright (c) 2010 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. Lochter & Merkle Informational [Page 1] RFC 5639 ECC Brainpool Standard Curves & Curve Generation March 2010 Table of Contents 1. Introduction ....................................................3 1.1. Scope and Relation to Other Specifications .................4 1.2. Requirements Language ......................................4 2. Requirements on the Elliptic Curve Domain Parameters ............4 2.1. Security Requirements ......................................5 2.2. Technical Requirements .....................................6 3. Domain Parameter Specification ..................................8 3.1. Domain Parameters for 160-Bit Curves .......................8 3.2. Domain Parameters for 192-Bit Curves .......................9 3.3. Domain Parameters for 224-Bit Curves ......................10 3.4. Domain Parameters for 256-Bit Curves ......................11 3.5. Domain Parameters for 320-Bit Curves ......................12 3.6. Domain Parameters for 384-Bit Curves ......................13 3.7. Domain Parameters for 512-Bit Curves ......................14 4. Object Identifiers and ASN.1 Syntax ............................15 4.1. Object Identifiers ........................................15 4.2. ASN.1 Syntax for Usage with X.509 Certificates ............16 5. Security Considerations ........................................17 6. Intellectual Property Rights ...................................18 7. References .....................................................18 7.1. Normative References ......................................18 7.2. Informative References ....................................19 Appendix A. Pseudo-Random Generation of Parameters ................22 A.1. Generation of Prime Numbers ................................22 A.2. Generation of Pseudo-Random Curves .........................24 Lochter & Merkle Informational [Page 2] RFC 5639 ECC Brainpool Standard Curves & Curve Generation March 2010 1. Introduction Although several standards for elliptic curves and domain parameters exist (e.g., [ANSI1], [FIPS], or [SEC2]), some major issues have still not been addressed: o Not all parameters have been generated in a verifiably pseudo- random way. In particular, the seeds from which the curve parameters were derived have been chosen ad hoc, leaving out an essential part of the security proof. o The primes selected for the base fields have a very special form facilitating efficient implementation. This does not only contradict the approach of pseudo-random parameters, but also increases the risk of implementations violating one of the numerous patents for fast modular arithmetic with special primes.Show full document text