Comparing the MOV and FR reductions in elliptic curve cryptography

Authors:
Ryuichi Harasawa;Junji Shikata;Joe Suzuki;Hideki Imai
Affiliations:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, Japan;Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, Japan;Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, Japan;Institute of Industrial Science, University of Tokyo, Tokyo, Japan
Venue:
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Year:
1999

Citing 8
Cited 4

Use of elliptic curves in cryptography

Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Nonsingular plane cubic curves over finite fields

Journal of Combinatorial Theory Series A
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves

Mathematics of Computation
Algorithmic number theory

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

Mathematics of Computation
Elliptic Curve Public Key Cryptosystems

Elliptic Curve Public Key Cryptosystems
A subexponential algorithm for discrete logarithms over the rational subgroup of the jacobians of large genus hyperelliptic curves over finite fields

ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Counting the number of points on elliptic curves over finite fields: strategies and performances

EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques

Characterization of Elliptic Curve Traces under FR-Reduction

ICISC '00 Proceedings of the Third International Conference on Information Security and Cryptology
The Generalized Weil Pairing and the Discrete Logarithm Problem on Elliptic Curves

LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
The generalized Weil pairing and the discrete logarithm problem on elliptic curves

Theoretical Computer Science - Latin American theorotical informatics
Implementation of cryptosystems based on Tate pairing

Journal of Computer Science and Technology

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper addresses the discrete logarithm problem in elliptic curve cryptography. In particular, we generalize the Menezes, Okamoto, and Vanstone (MOV) reduction so that it can be applied to some non-supersingular elliptic curves (ECs); decrypt Frey and Rück (FR)'s idea to describe the detail of the FR reduction and to implement it for actual elliptic curves with finite fields on a practical scale; and based on them compare the (extended) MOV and FR reductions from an algorithmic point of view. (This paper has primarily an expository role.)