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IETF RFC 6090
[ACTIVE]

Fundamental Elliptic Curve Cryptography Algorithms

Metadata

Publisher
IETF
Doc Type
Informational
Pages
34
Abstract
This note describes the fundamental algorithms of Elliptic Curve Cryptography (ECC) as they were defined in some seminal references from 1994 and earlier. These descriptions may be useful for implementing the fundamental algorithms without using any of the specialized methods that were developed in following years. Only elliptic curves defined over fields of characteristic greater than three are in scope; these curves are those used in Suite B. This document is not an Internet Standards Track specification; it is published for informational purposes.
Publication Date
2011-02-01
Status Note
Informational
DOI
10.17487/RFC6090
Link
https://doi.org/10.17487/RFC6090
Author(s)
David McGrew
Kevin Igoe
Margaret Salter
Keyword(s)
ECC
Latest version of IETF RFC 6090

Document Versions — IETF RFC 6090

  • ▶ IETF RFC 6090 (2011-02-01)
    THIS DOC [ACTIVE] [LATEST VERSION]

Normative Reference(s)

  • Diffie, W. and M. Hellman, "New Directions in Cryptography", IEEE Transactions in Information Theory IT-22, pp. 644-654, 1976. EXTERNAL
  • Menezes, A., Vanstone, S., and T. Okamoto, "Reducing Elliptic Curve Logarithms to Logarithms in a Finite Field", IEEE Transactions on Information Theory Vol. 39, No. 5, pp. 1639-1646, September, 1993. EXTERNAL
  • Deskins, W., "Abstract Algebra", MacMillan Company New York, 1966. EXTERNAL
  • Agnew, G., Mullin, R., and S. Vanstone, "Improved Digital Signature Scheme based on Discrete Exponentiation", Electronics Letters Vol. 26, No. 14, July, 1990. EXTERNAL
  • Horster, P., Michels, M., and H. Petersen, "Meta-ElGamal signature schemes", University of Technology Chemnitz- Zwickau Department of Computer Science, Technical Report TR-94-5, May 1994. EXTERNAL
  • Koyama, K. and Y. Tsuruoka, "Digital signature system based on elliptic curve and signer device and verifier device for said system", Japanese Unexamined Patent Application Publication H6-43809, February 18, 1994. EXTERNAL
  • Koblitz, N., "Elliptic Curve Cryptosystems", Mathematics of Computation, Vol. 48, 1987, pp. 203-209, 1987. EXTERNAL
  • Miller, V., "Use of elliptic curves in cryptography", Advances in Cryptology - CRYPTO '85 Proceedings, Springer Lecture Notes in Computer Science (LNCS), volume 218, 1985. EXTERNAL
  • Knuth, D., "The Art of Computer Programming, Vol. 2: Seminumerical Algorithms", Addison Wesley , 1981. EXTERNAL
  • Silverman, J., "The Arithmetic of Elliptic Curves", Springer-Verlag, New York, 1986. EXTERNAL
  • Frey, G. and H. Ruck, "A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves.", Mathematics of Computation Vol. 62, No. 206, pp. 865-874, 1994. EXTERNAL
  • Massey, J., "Logarithms in finite cyclic groups - cryptographic issues", Proceedings of the 4th Symposium on Information Theory, 1983. EXTERNAL
  • Chudnovsky, D. and G. Chudnovsky, "Sequences of numbers generated by addition in formal groups and new primality and factorization tests", Advances in Applied Mathematics, Volume 7, Issue 4, December 1986. EXTERNAL
  • Bender, A. and G. Castagnoli, "On the Implementation of Elliptic Curve Cryptosystems", Advances in Cryptology - CRYPTO '89 Proceedings, Springer Lecture Notes in Computer Science (LNCS), volume 435, 1989. EXTERNAL
  • RSA.PKCS1.v1.5.1993 — PKCS1 EXTERNAL

Bibliographic Reference(s)

  • ANSI.X9.62 — X9.62 EXTERNAL
  • NIST FIPS 180-2 [Withdrawn]
  • NIST.FIPS.186 — DSS EXTERNAL
  • Pollard, J., "Monte Carlo methods for index computation mod p", Mathematics of Computation, Vol. 32, 1978. EXTERNAL
  • Pohlig, S. and M. Hellman, "An Improved Algorithm for Computing Logarithms over GF(p) and its Cryptographic Significance", IEEE Transactions on Information Theory, Vol. 24, pp. 106-110, 1978. EXTERNAL
  • ElGamal, T., "Cryptography and logarithms over finite fields", Advances in Cryptology - CRYPTO '84 Proceedings, Springer Lecture Notes in Computer Science (LNCS), volume 196, 1984. EXTERNAL
  • Anderson, J., "Response to the proposed DSS", Communications of the ACM, v. 35, n. 7, p. 50-52, July 1992. EXTERNAL
  • Branstad, D. and M. Smid, "Response to Comments on the NIST Proposed Digital Signature Standard", Advances in Cryptology - CRYPTO '92 Proceedings, Springer Lecture Notes in Computer Science (LNCS), volume 740, August 1992. EXTERNAL
  • Anderson, R. and S. Vaudenay, "Minding Your P's and Q's", Advances in Cryptology - ASIACRYPT '96 Proceedings, Springer Lecture Notes in Computer Science (LNCS), volume 1163, 1996. EXTERNAL
  • Lim, C. and P. Lee, "A Key Recovery Attack on Discrete Log-based Schemes Using a Prime Order Subgroup", Advances in Cryptology - CRYPTO '97 Proceedings, Springer Lecture Notes in Computer Science (LNCS), volume 1294, 1997. EXTERNAL
  • Biehl, I., Meyer, B., and V. Muller, "Differential fault analysis on elliptic curve cryptosystems", Advances in Cryptology - CRYPTO 2000 Proceedings, Springer Lecture Notes in Computer Science (LNCS), volume 1880, 2000. EXTERNAL
  • "Standard Specifications for Public Key Cryptography", Institute of Electric and Electronic Engineers (IEEE), P1363, 2000. EXTERNAL
  • U.S. National Institute of Standards and Technology, "DIGITAL SIGNATURE STANDARD", Federal Register, Vol. 56, August 1991. EXTERNAL
  • Vaudenay, S., "Hidden Collisions on DSS", Advances in Cryptology - CRYPTO '96 Proceedings, Springer Lecture Notes in Computer Science (LNCS), volume 1109, 1996. EXTERNAL
  • Nyberg, K. and R. Rueppel, "Message Recovery for Signature Schemes Based on the Discrete Logarithm Problem", Advances in Cryptology - EUROCRYPT '94 Proceedings, Springer Lecture Notes in Computer Science (LNCS), volume 950, May 1994. EXTERNAL
  • U. S. National Security Agency (NSA), "NSA Suite B Cryptography", < http://www.nsa.gov/ia/programs/ suiteb_cryptography/index.shtml >. EXTERNAL
  • ElGamal, T., "A public key cryptosystem and a signature scheme based on discrete logarithms", IEEE Transactions on Information Theory, Vol. 30, No. 4, pp. 469-472, 1985. EXTERNAL
  • Koyama, K., Maurer, U., Vanstone, S., and T. Okamoto, "New Public-Key Schemes Based on Elliptic Curves over the Ring Zn", Advances in Cryptology - CRYPTO '91 Proceedings, Springer Lecture Notes in Computer Science (LNCS), volume 576, 1991. EXTERNAL
  • Rivest, R., "Response to the proposed DSS", Communications of the ACM, v. 35, n. 7, p. 41-47, July 1992. EXTERNAL
  • Lehmer, D., "Computer technology applied to the theory of numbers", M.A.A. Studies in Mathematics, 180-2, 1969. EXTERNAL
  • Rose, H., "A Course in Number Theory", Oxford University Press, 1988. EXTERNAL
  • Horster, P. and H. Petersen, "Verallgemeinerte ElGamal- Signaturen", Proceedings der Fachtagung SIS '94, Verlag der Fachvereine, Zurich, 1994. EXTERNAL
  • van Oorschot, P. and M. Wiener, "On Diffie-Hellman key agreement with short exponents", Advances in Cryptology - EUROCRYPT '96 Proceedings, Springer Lecture Notes in Computer Science (LNCS), volume 1070, 1996. EXTERNAL
  • van Oorschot, P. and M. Wiener, "Parallel Collision Search with Application to Hash Functions and Discrete Logarithms", Proceedings of the 2nd ACM Conference on Computer and communications security, pp. 210-218, 1994. EXTERNAL
  • ElGamal, T., "Cryptography and logarithms over finite fields", Stanford University, UMI Order No. DA 8420519, 1984. EXTERNAL
  • Knuth, D., "The Art of Computer Programming, Vol. 3: Sorting and Searching", Addison Wesley, 1981. EXTERNAL
  • IETF RFC 2119 [Active*]
  • IETF RFC 2409 [Superseded*]
  • IETF RFC 2412 [Active*]
  • IETF RFC 3979 [Superseded*]
  • IETF RFC 4086 [Active*]
  • IETF RFC 4306 [Superseded*]
  • IETF RFC 4753 [Superseded*]
  • IETF RFC 4754 [Active*]
  • IETF RFC 4879 [Superseded*]
  • IETF RFC 5114 [Active*]
  • IETF RFC 5903 [Active*]
  • IETF RFC 5996 [Superseded*]
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