Abstract
McCurley's key agreement scheme is a variation on the well known Diffie-Hellman scheme with enhanced security. In McCurley's scheme a successful attacker must be able to break the ordinary Diffie-Hellman scheme and also factorise large numbers. This paper presents an analogue of McCurley's scheme using elliptic curves. A consequence is that a method to break ordinary Diffie-Hellman would not be applicable to our scheme. An advantage of our scheme over McCurley's is that much smaller key lengths can be used.
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References
N.Demytko, “A New Elliptic curve Based Analogue of RSA”, Advances in Cryptology — EUROCRYPT 93, pp. 40–49, Springer-Verlag, 1994.
W. Diffie and M. Hellman, “New Directions in Cryptography”, IEEE Transactions on Information Theory, 22, pp. 644–654, (1976).
K. Koyama, U.M. Maurer, T. Okamoto, S.A. Vanstone, “New Public-Key Schemes Based on Elliptic Curves over the Ring Zn”, Proceedings of Crypto 91, pp. 252–266, Springer-Verlag, 1992.
G. Lay and H. Zimmer, “Constructing elliptic curves with given group order over large finite fields”, Algorithmic Number Theory: First International Symposium, Lecture Notes in Computer Science, 877, Springer-Verlag, pp. 250–263.
H.W. Lenstra, Jr., “Factoring with Elliptic Curves”, Annals of Mathematics, 126, pp. 649–673, 1987.
U.M. Maurer, “Towards the Equivalence of Breaking the Diffie-Hellman Proto col and Computing Discrete Logarithms”, Proceedings of Crypto '94, pp. 271–281, Springer-Verlag, 1994.
K. S. McCurley, “A Key Distribution Scheme Equivalent to Factoring”, Journal of Cryptology, Vol. 1, No. 2 (1988).
A. Menezes, Elliptic Curve Public Key Cryptosystems, Kluwer Academic Publishers (1993).
A. Menezes, T. Okamoto and S.A. Vanstone, “Reducing Elliptic Curve Logarithms to Logarithms in a Finite Field”, IEEE Transactions on Information Theory, (39), 1993, pp. 1639–1646.
P.C. van Oorschot, “A Comparison of Practical Public Key Cryptosystems Based on Integer Factorization and Discrete Logarithms”, in G.J.Simmons (Ed.), Contemporary Cryptology, IEEE Press 1992.
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© 1995 Springer-Verlag Berlin Heidelberg
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Smith, A., Boyd, C. (1995). An elliptic curve analogue of McCurley's key agreement scheme. In: Boyd, C. (eds) Cryptography and Coding. Cryptography and Coding 1995. Lecture Notes in Computer Science, vol 1025. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60693-9_17
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DOI: https://doi.org/10.1007/3-540-60693-9_17
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