ANALYSIS OF SMOOTH NUMBERS SEARCH METHODS FOR SOLVING THE DISCRETE LOGARITHM PROBLEM

Abstract

This paper describes the formulation of the discrete logarithm problem, which is an important mathematical problem. The algorithm for computing the discrete logarithm of Silver-Pohlig-Hellman is analyzed and its drawbacks arising from the use of numbers of a special type, called smooth, are indicated. The concept of a smooth prime number was introduced, a classification was introduced depending on the increase of the successive factors on the perfectly smooth and partially smooth prime numbers. It is shown that to search for smooth primes and analyze their properties, it is necessary to know how primes are distributed depending on the number of simple factors. The problem of constructing a measure of smoothness is given.