English

Finding discrete logarithm in $F_p^* $

Number Theory 2021-04-30 v2 Discrete Mathematics

Abstract

Difficulty of calculation of discrete logarithm for any arbitrary Field is the basis for security of several popular cryptographic solutions. Pohlig-Hellman method is a popular choice to calculate discrete logarithm in finite field FpF_p^*. Pohlig-Hellman method does yield good results if p is smooth ( i.e. p-1 has small prime factors). We propose a practical alternative to Pohlig-Hellman algorithm for finding discrete logarithm modulo prime. Although, proposed method, similar to Pohlig-Hellman reduces the problem to group of orders pip_i for each prime factor and hence in worst case scenario (including when p=2q+1 , q being another prime) order of run time remains the same. However in proposed method, as there is no requirement of combining the result using Chinese Remainder Theorem and do the other associated work ,run times are much faster.

Keywords

Cite

@article{arxiv.2104.13310,
  title  = {Finding discrete logarithm in $F_p^* $},
  author = {Rajeev Kumar},
  journal= {arXiv preprint arXiv:2104.13310},
  year   = {2021}
}

Comments

Additional python code file in pdf format

R2 v1 2026-06-24T01:34:14.851Z