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References

[Blaze] M. Blaze, "A better DES challenge", presentation at the rump session at Crypto '97.

[Certicom] Certicom Corp. white paper, "Remarks on the security of the elliptic curve cryptosystem", September 1997.

[Escott] A. Escott, Attacking Elliptic Curve Cyrptosystems using the Parallel Pollard rho method. Preprint, 1998.

[FR] G. Frey and H. Rück, "A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves", Mathematics of Computation, volume 62, pages 865-874, 1994.

[GLV] R. Gallant and R. Lambert and S. Vanstone. Improving the parallelized Pollard lambda search on binary anomalous curves, preprint, 1998.

[HMV] G. Harper, A. Menezes and S. Vanstone, "Public-key cryptosystems with very small key lengths", Advances in Cryptology EUROCRYPT '92, Lecture Notes in Computer Science, volume 658, Springer-Verlag, pages 163-173, 1993.

[Koblitz] N. Koblitz, "Elliptic curve cryptosystems", Mathematics of Computation, volume 48, pages 203-209, 1987.

[Koblitz2] N. Koblitz, "CM-curves with good cryptographic properties", Advances in Cryptology CRYPTO '91, Lecture Notes in Computer Science, volume 576, Springer-Verlag, pages 279-287, 1992.

[Koblitz3] N. Koblitz, A Course in Number Theory and Cryptography, Springer-Verlag, 2nd edition, 1994.

[LN] R. Lidl and H. Niederreiter, Introduction to Finite Fields and their Applications, Cambridge University Press, 1994.

[McEliece] R. McEliece, Finite Fields for Computer Scientists and Engineers, Kluwer Academic Publishers, 1987.

[Menezes] A. Menezes, Elliptic Curve Pub1ic Key Cryptosystems, Kluwer Academic Publishers, 1993.

[MVV] A. Menezes, P. van Oorschot and S. Vanstone, Handbook of Applied Cryptography, CRC Press, 1997.

[MOV] A. Menezes, T. Okamoto and S. Vanstone, "Reducing elliptic curve logarithms to logarithms in a finite field", IEEE Transactions on Information Theory, volume 39, pages 1639-1646, 1993.

[Miller] V. Miller, "Uses of elliptic curves in cryptography", Advances in Cryptology - CRYPTO '85, Lecture Notes in Computer Science, volume 218, Springer-Verlag, pages 417-426, 1986.

[VW] P. van Oorschot and M. Wiener, "Parallel collision search with cryptanalytic applications", to appear in Journal of Cryptology. (An earlier version appeared in the Proceedings of the 2nd ACM Conference on Computer and Communications Security, ACM Press, pages 210-218, 1994.)

[PH] S. Pohlig and M. Hellman, "An improved algorithm for computing logarithms over GF(p) and its cryptographic significance", IEEE Transactions on Information Theory, volume 24, pages 106-110, 1978.

[Pollard] J. Pollard, "Monte Carlo methods for index computation mod p", Mathematics of Computation, volume 32, pages 918-924, 1978.

[SA] T. Satoh and K. Arako, "Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves", preprint, 1997

[SHA-1] FIPS 180-1, "Secure hash standard", Federal Information Processing Standards Publication 180-1, U.S. Department of Commerce/N.I.S.T., April 1995.

[Solinas], J. Solinas, "An improved algorithm for arithmetic on a family of elliptic curves", Advances in Cryptology - CRYPTO '97, Lecture Notes in Computer Science, volume 1294, Springer-Verlag, pages 357-371, 1997.

[Smart] N. Smart. Announcement in the NMBRTHRY-List of an attack on the ECDLP for anomalous elliptic curves, 30 Sep 1997.

[SS] J.H. Silverman and J. Suzuki. Elliptic curve discrete logarithms and the index calculus. To appear in the proceedings of ASIACRYPT ’98.

[Teske] E. Teske. Speeding up Pollard's rho method for computing discrete logarithms. In Algorithmic Number Theory ANTS-III, volume 1423 of Lecture Notes in Computer Science, pages 541-554, 1998.

[X962] ANSI X9.62, "The elliptic curve digital signature algorithm (ECDSA)", draft standard, 1997.

[X963] ANSI X9.63, "Elliptic curve key agreement and transport protocols", draft standard, 1997.

 

 

 


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