Implementation Analysis of Index Calculus Method on Elliptic Curves over Prime Finite Fields

EasyChair Preprint 15613

Abstract

In 2016,Petit et al. first studied the implementation of the index product method on elliptic curves in finite fields of prime numbers, and in 2018, Momonari and Kudo et al. improved Petit et al. algorithm. This paper analyzes the research results of Petit, Momonari and Kudo, and points out the existing problems of the algorithm. Therefore, with the help of polynomial function and index calculus, a pseudo-index product algorithm for elliptic curve discrete logarithm problem over prime finite fields is proposed, and its correctness is analyzed and verified. It is pointed out that there is no method to solve the subexponential discrete logarithm on elliptic curve over prime finite fields, or at least in the present research background, there is no method to solve the subexponential discrete logarithm.

Keyphrases: decomposition base, discrete logarithm, factorization, prime finite fields, smooth boundary

@booklet{EasyChair:15613,
  author    = {Jianjun Hu},
  title     = {Implementation Analysis of Index Calculus Method on Elliptic Curves over Prime Finite Fields},
  howpublished = {EasyChair Preprint 15613},
  year      = {EasyChair, 2024}}