The Discrete Logarithms and the Algorithms (Qi Cheng)

Abstract

Many cryptography protocols rely on hard computational number theoretical problems for security. The discrete logarithm problem over finite fields or elliptic curves is one of the most important candidates, besides the integer factorization problem.

In this talk, I will first survey several algorithms attacking the discrete logarithms over finite fields, starting from generic algorithms and the index calculus. My discussion will then be focusing on the recent approach of quasi-polynomial-time descending, and the relationship between the discrete logarithm problem and the Reed-Solomon decoding problem.

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