Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Computation of discrete logarithms in prime fields
Designs, Codes and Cryptography
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Computing canonical heights with little (or no) factorization
Mathematics of Computation
Mathematics of Computation
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
On Ordinary Elliptic Curve Cryptosystems
ASIACRYPT '91 Proceedings of the International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Computing Discrete Logarithms with the General Number Field Sieve
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Discrete Logarithms: The Effectiveness of the Index Calculus Method
ANTS-II Proceedings of the Second 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
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
A Note on Security Proofs in the Generic Model
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
A survey of local and global pairings on elliptic curves and abelian varieties
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
On partial lifting and the elliptic curve discrete logarithm problem
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Algebraic curves and cryptography
Finite Fields and Their Applications
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The discrete logarithm problem forms the basis of numerous cryptographic systems. The most effective attack on the discrete logarithm problem in the multiplicative group of a finite field is via the index calculus, but no such method is known for elliptic curve discrete logarithms. Indeed, Miller [23] has given a brief heuristic argument as to why no such method can exist. IN this note we give a detailed analysis of the index calculus for elliptic curve discrete logarithms, amplifying and extending miller's remarks. Our conclusions fully support his contention that the natural generalization of the index calculus to the elliptic curve discrete logarithm problem yields an algorithm with is less efficient than a brute-force search algorithm.