Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p

Mathematics of Computation

Volumn 67, Issue 221, 1998, Pages 353-356

  Semaev, I A ^a  

^a NONE   (Russian Federation)

Author keywords

Cryptography; Discrete logarithms; Elliptic curves

Indexed keywords

EID: 0032352723     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-98-00887-4     Document Type: Article

References (10)

1. V. Miller, Use of elliptic curves in cryptography, Advances in Cryptology - Crypto '85, Springer-Verlag, New York, 1986, 417-426. MR 88b:68040
2. N. Koblitz, Elliptic curve cryptosystems, Math. Comp. 48 (1987). 203-209. MR 88b:94017
3. A. Menezes, S. Vanstone, and O. Tatsuaki, Reducing elliptic curve logarithms to logarithms in a finite field, Proc. 23rd ACM Sympos. Theory of Computing, 1991, pp. 80-89.
4. Vi. A. CeMaes, Btiicmpinil euizopumM euHuc.ienun cnapuaamur A. Beü.w na MAurimmecKou Kpuaoù, International Conference "Modern Problems in Number Theory", Russia, Tula, Sept. 20-25, 1993, Abstracts of papers.
5. G. Frey and H.-G. Ruck, A remark concerning m-divisibility and the discrete logarithm, in the divisor class group of curves, Math. Comp. 62 (1994), 865-874. MR 94h:11056
6. S. Pohlig and M. Hellman, An improved algorithm for computing logarithms over GF(p) and its cryptographic significance, IEEE Trans. Inform. Theory, IT-24 (1978). 106-110. MR 58:4617
7. J. M. Pollard, Monte-Carlo methods for index computation (mod p), Math. Comp. 32 (1978), 918-924. MR 58:10684
8. J. H. Silverman, The arithmetic of elliptic curves, Springer-Verlag, 1986. MR 87g:11070
9. J. P. Serre, Sur la topologie des variétés algébriques en caractéristique p, Sympos. Internac. Topologia Algebraica, Mexico City, 1956, 24-53. MR 20:4559
10. H.-G. Ruck, A remark on the paper "Evaluation of discrete logarithms on some elliptic curves, by I. A. Semaev", communication to "Mathematics of Computation".