The Xedni Calculus and the Elliptic Curve Discrete LogarithmProblem

Authors:
Joseph H. Silverman
Affiliations:
Mathematics Department, Box 1917, Brown University,, Providence, RI 02912
Venue:
Designs, Codes and Cryptography
Year:
2000

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Abstract

Let E/\ff_p be an ellipticcurve defined over a finite field, and let S,T\in E(\ff_p)be two points on E. The Elliptic Curve DiscreteLogarithm Problem (ECDLP) asks that an integer mbe found so that S=mT in E(\ff_p).In this note we give a new algorithm, termed the Xedni Calculus,which might be used to solve the ECDLP. As remarked by Neal Koblitz,the Xedni method is also applicable to the classical discretelogarithm problem for \ff_p^* and to the integerfactorization problem.