On partial lifting and the elliptic curve discrete logarithm problem

Authors:
Qi Cheng;Ming-Deh Huang
Affiliations:
School of Computer Science, The University of Oklahoma, Norman, OK;Computer Science Department, University of Southern California, Los Angeles, CA
Venue:
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Year:
2004

Citing 9
Cited 0

Use of elliptic curves in cryptography

Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Algorithms for modular elliptic curves

Algorithms for modular elliptic curves
Computing canonical heights with little (or no) factorization

Mathematics of Computation
Analysis of the Xedni Calculus Attack

Designs, Codes and Cryptography
Analysis of the Weil Descent Attack of Gaudry, Hess and Smart

CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Elliptic Curve Discrete Logarithms and the Index Calculus

ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Discrete Logarithms: The Effectiveness of the Index Calculus Method

ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Lifting Elliptic Curves and Solving the Elliptic Curve Discrete Logarithm Problem

ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
A subexponential algorithm for the discrete logarithm problem with applications to cryptography

SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

It has been suggested that a major obstacle in finding an index calculus attack on the elliptic curve discrete logarithm problem lies in the difficulty of lifting points from elliptic curves over finite fields to global fields We explore the possibility of circumventing the problem of explicitly lifting points by investigating whether partial information about the lifting would be sufficient for solving the elliptic curve discrete logarithm problem Along this line, we show that the elliptic curve discrete logarithm problem can be reduced to three partial lifting problems Our reductions run in random polynomial time assuming certain conjectures are true These conjectures are based on some well-known and widely accepted conjectures concerning the expected ranks of elliptic curves over the rationals.