Elliptic curve cryptographic systems

Part of book or chapter of book, Article English OPEN
Andreas Enge (2013)
  • Publisher: Chapman and Hall/CRC
  • Journal: Handbook of Finite Fields
  • Subject: [ MATH.MATH-NT ] Mathematics [math]/Number Theory [math.NT] | [ INFO.INFO-CR ] Computer Science [cs]/Cryptography and Security [cs.CR] | elliptic curves | cryptology
    acm: ComputingMilieux_MISCELLANEOUS

International audience
  • References (72)
    72 references, page 1 of 8

    September 1998. Available at http://grouper.ieee.org/groups/1363/private/ x9-62-09-20-98.zip.

    [2] ANSI. Key agreement and key transport using elliptic curve cryptography. Working Draft American National Standard: Public Key Cryptography for the Financial Services Industry X9.63-199x, American National Standards Institute, January 1999. Available at http://grouper.ieee.org/groups/1363/private/ x9-63-01-08-99.zip.

    [3] R. Balasubramanian and Neal Koblitz. The improbability that an elliptic curve has subexponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm. J. Cryptology, 11(2):141{145, 1998.

    [4] Paulo S. L. M. Barreto, Steven D. Galbraith, Colm O'hEigeartaigh, and Michael Scott. E cient pairing computation on supersingular abelian varieties. Designs, Codes and Cryptography, 42:239{271, 2007.

    [5] Juliana Belding, Reinier Broker, Andreas Enge, and Kristin Lauter. Computing Hilbert class polynomials. In Alf van der Poorten and Andreas Stein, editors, Algorithmic Number Theory | ANTS-VIII, volume 5011 of Lecture Notes in Computer Science, pages 282{295, Berlin, 2008. Springer-Verlag.

    [6] Mihir Bellare and Phillip Rogaway. Minimizing the use of random oracles in authenticated encryption schemes. In Yongfei Han, Tatsuaki Okamoto, and Sihan Qing, editors, Information and Communications Security, volume 1334 of Lecture Notes in Computer Science, pages 1{16, Berlin, 1997. Springer-Verlag.

    [7] I. F. Blake, G. Seroussi, and N. P. Smart. Elliptic curves in cryptography, volume 265 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 2000. Reprint of the 1999 original.

    [8] Ian F. Blake, Gadiel Seroussi, and Nigel P. Smart. Advances in Elliptic Curve Cryptography, volume 317 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 2005.

    [9] Dan Boneh, Eu-Jin Goh, and Kobbi Nissim. Evaluating 2-DNF formulas on ciphertexts. In Joe Kilian, editor, Theory of Cryptography | TCC 2005, volume 3378 of Lecture Notes in Computer Science, pages 325{341, Berlin, 2005. Springer-Verlag.

    [10] A. Bostan, F. Morain, B. Salvy, and E. Schost. Fast algorithms for computing isogenies between elliptic curves. Mathematics of Computation, 77(263):1755{1778, 2008.

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