Comparing the MOV and FR reductions in elliptic curve cryptography

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1592, Issue , 1999, Pages 190-205

  Harasawa, Ryuichi ^a   Shikata, Junji ^a   Suzuki, Joe ^a   Imai, Hideki ^b  

^a OSAKA UNIVERSITY   (Japan)

^b INSTITUTE OF INDUSTRIAL SCIENCE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CRYPTOGRAPHY; GEOMETRY; PUBLIC KEY CRYPTOGRAPHY;

DISCRETE LOGARITHM PROBLEMS; ELLIPTIC CURVE; ELLIPTIC CURVE CRYPTOGRAPHY; FINITE FIELDS; NON-SUPERSINGULAR; OKAMOTO;

CURVE FITTING;

EID: 84957667771     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-48910-X_14     Document Type: Conference Paper

References (25)

1. L. Adleman, J. DeMarrais, and M. Huang, A subexponential algorithm for discrete logarithms over the rational subgroup of the Jacobians of large genus hyperelliptic curves over finite fields, Algorithmic Number Theory, Lecture Notes in Computer Science, volume 877, Springer-Verlag, 1994, pp. 28-40.
2. A. O. Atkin, The number of points on an elliptic curve modulo a prime, preprint, 1988.
3. A. Atkin and F. Morain, Elliptic curves and primality proving, Mathematics of Computation 61 (1993), 29-68.
4. E. Bach,Algorithmic Number Theory,Volume 1; Efficient Algorithms, MIT Press, Cambridge, Massachusetts, 1996.
5. R. Balasubramanian and N. Koblitz, The improbability that an elliptic curve has subexponential discrete log problem under the Menezes-Okamoto-Vanstone algo- rithm, Journal of Cryptography 11 (1998), 141-145.
6. N. Elkies, Explicit isogenies, preprint, 1991.
7. G. Frey and H. Rück, A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves, Mathematics of Computation 62 (1994), 865- 874.
8. M. Kac, On the notion of recurrence in discrete stochastic processes, Ann. of Math. Statist., 53 (1947), 1002-1010.
9. N. Koblitz, Elliptic curve cryptosystems, Mathematics of Computation 48 (1987), 203-209.
10. N. Koblitz, A Course in Number Theory and Cryptography, Springer-Verlag, New York, 2nd edition, 1996.
11. H. W. Lenstra, Factoring integers with elliptic curves. Annals of Mathematics, 126 (1987), 649-673.
12. R. Lercier and F. Morain, Counting the number of points on elliptic curves over finite fields: strategy and performance, Advances in Cryptology, EUROCRYPT'95, Lecture Notes in Computer Science 921 (1995), 79-94.
13. A. Menezes, T. Okamoto, and S. Vanstone, Reducing elliptic curve logarithms to logarithms in a finite field, IEEE Transactions on Information Theory 39 (1993), 1639-1646.
14. A. Menezes, Elliptic curve public key cryptosystems, Kluwer Academic Publishes (1994).
15. V. S. Miller, Use of elliptic curves in cryptography, Advances in Cryptography CRYPTO '85 (Lecture Notes in Computer Science, vol 218), Springer-Verlag, 1986, pp. 417-426.
16. V. Miller, Short program for functions on curves, unpublished manuscript, 1986.
17. S. C. Pohlig and M. E. Hellman, An improved algorithm for computing logarithms over GF(p) and its cryptographic significance, IEEE Transactions on Information Theory, 24 (1978),pp 106-110.
18. T. Satoh and K. Araki, Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves, Commentarii Math,Univ,Saniti Pauli, 47,1,pp 88 - 92 (1998).
19. R. Schoof, Nonsingular plane cubic curves over finite fields, Journal of Combination Theory, Vol. A. 46 (1987), 183-211.
20. R. Schoof, Elliptic curves over finite fields and the computation of square roots modulo p Math. Comp. 44 (1985), 483-494.
21. I. Semaev, Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p, Mathematics of Computation 67 (1998), 353-356.
22. J. H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Math., vol. 106, Springer-Verlag, Berlin and New York, 1994.
23. J. H. Silverman, J. Suzuki, Elliptic curve discrete logarithms and index calculus, ASIACRYPT'98 (Lecture Notes in Computer Science), to appear.
24. N. Smart, The discrete logarithm problem on elliptic curves of trace one, preprint, 1997.
25. J. Tate, WC-groups over p-adic fields, ann Sci. Ecole, Norm. Sup. 2 (1969), 521-560