The Xedni calculus and the elliptic curve discrete logarithm problem

Let E/F-p be an elliptic curve defined over a finite field, and let S,T is an element of E(F-p) be two points on E. The Elliptic Curve Discrete Logari thm Problem (ECDLP) asks that an integer m be found so that S = mT in E(F-p ). In this note we give a new algorithm, termed the Xedni Calculus, which m ight be used to solve the ECDLP. As remarked by Neal Koblitz, the Xedni met hod is also applicable to the classical discrete logarithm problem for F-p* and to the integer factorization problem.