The Xedni Calculus and the Elliptic Curve Discrete Logarithm Problem

AbstractLet $$E/{\mathbb{F}}_P$$ be an elliptic curve defined over a finite field, and let $$S,T \in E({\mathbb{F}}_P )$$ be two points on E. The Elliptic Curve Discrete Logarithm Problem (ECDLP) asks that an integer m be found so that S=mT in $$E({\mathbb{F}}_P )$$ . 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 discrete logarithm problem for $${\mathbb{F}}_p^*$$ and to the integer factorization problem.