Nonsingular plane cubic curves over finite fields
Journal of Combinatorial Theory Series A
Computing canonical heights with little (or no) factorization
Mathematics of Computation
Algebraic aspects of cryptography
Algebraic aspects of cryptography
The Xedni Calculus and the Elliptic Curve Discrete LogarithmProblem
Designs, Codes and Cryptography
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
Use of Elliptic Curves in Cryptography
CRYPTO '85 Advances in Cryptology
Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
The State of Elliptic Curve Cryptography
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
The Xedni Calculus and the Elliptic Curve Discrete LogarithmProblem
Designs, Codes and Cryptography
Journal of Symbolic Computation
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
Signature calculus and discrete logarithm problems
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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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Thexedni calculus attack on the elliptic curve discrete logarithmproblem (ECDLP) involves lifting points from the finite field{\Bbb F}_p to the rational numbers {\Bbb Q}and then constructing an elliptic curve over {\Bbb Q}that passes through them. If the lifted points are linearly dependent,then the ECDLP is solved. Our purpose is to analyze the practicalityof this algorithm. We find that asymptotically the algorithmis virtually certain to fail, because of an absolute bound onthe size of the coefficients of a relation satisfied by the liftedpoints. Moreover, even for smaller values of p experimentsshow that the odds against finding a suitable lifting are prohibitivelyhigh.