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The implementation of elliptic curve cryptosystems

  • Section 1 Public-Key Cryptosystems
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Advances in Cryptology — AUSCRYPT '90 (AUSCRYPT 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 453))

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Abstract

Elliptic curves have been studied for many years. Recent interest has revolved around their applicability to factoring integers and to cryptography. In this paper we explore the feasibility of implementing in hardware an arithmetic processor for doing elliptic curve computations over fields of characteristic two. The elliptic curve analogue of the ElGamal cryptosystem is also analyzed.

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References

  1. G. Agnew, T. Beth, R. Mullin, and S. Vanstone, “Arithmetic operations in GF(2m), submitted to Journal of Cryptology.

    Google Scholar 

  2. G. Agnew, R. Mullin, I. Onyszchuk and S. Vanstone, “An implementation for a fast public key cryptosystem”, to appear.

    Google Scholar 

  3. D. Ash, I. Blake and S. Vanstone, “Low complexity normal bases”, Discrete Applied Mathematics, 25 (1989), 191–210.

    Google Scholar 

  4. W. Diffie and M. Hellman, “New directions in cryptography”, IEEE Transactions on Information Theory, 22 (1976), 644–654.

    Google Scholar 

  5. T. ElGamal, “A public key cryptosystem and a signature scheme based on discrete logarithms”, IEEE Transactions on Information Theory, 31 (1985), 469–472.

    Google Scholar 

  6. J. Hastad, “On using RSA with low exponent in a public key network”, Advances in Cryptology: Proceedings of Crypto '85, Lecture Notes in Computer Science, 218 (1986), Springer Verlag, 403–408.

    Google Scholar 

  7. N. Koblitz, “Elliptic curve cryptosystems”, Mathematics of Computation, 48 (1987), 203–209.

    Google Scholar 

  8. N. Koblitz, Course in Number Theory and Cryptography, Springer-Verlag, New York, 1987.

    Google Scholar 

  9. A. Menezes and S. Vanstone, “Isomorphism classes of elliptic curves over finite fields”, Research Report CORR 90-1, Department of Combinatorics and Optimization, University of Waterloo, January 1990.

    Google Scholar 

  10. V. Miller, “Uses of elliptic curves in cryptography”, Advances in Cryptology: Proceedings of Crypto '85, Lecture Notes in Computer Science, 218 (1986), Springer Verlag, 417–426.

    Google Scholar 

  11. P. Montgomery, “Speeding the Pollard and elliptic curve methods of factorization”, Mathematics of Computation, 48 (1987), 243–264.

    Google Scholar 

  12. R. Mullin, I. Onyszchuk, S. Vanstone and R. Wilson, “Optimal normal bases in GF(p n)”, Discrete Applied Mathematics, 22 (1988/89), 149–161.

    Google Scholar 

  13. T. Rosati, “A high speed data encryption processor for public key cryptography”, Proceedings of IEEE Custom Integrated Circuits Conference, San Diego (1989), 12.3.1–12.3.5.

    Google Scholar 

  14. J. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, New York, 1986.

    Google Scholar 

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Jennifer Seberry Josef Pieprzyk

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© 1990 Springer-Verlag Berlin Heidelberg

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Menezes, A., Vanstone, S. (1990). The implementation of elliptic curve cryptosystems. In: Seberry, J., Pieprzyk, J. (eds) Advances in Cryptology — AUSCRYPT '90. AUSCRYPT 1990. Lecture Notes in Computer Science, vol 453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030345

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  • DOI: https://doi.org/10.1007/BFb0030345

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53000-8

  • Online ISBN: 978-3-540-46297-2

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