Solving the DLP with low hamming weight product exponents and improved attacks on the GPS identification scheme

Abstract

This paper describes methods of solving certain parameters of the discrete logarithm problem with low Hamming weight product exponents. Our approach is shown to be applicable for a concrete analysis of the GPS identification scheme. To achieve this, we introduce the notion of parameters dependent splitting system which served as tools to yield two improved results. The first attains a lower time complexity over the current state of the art without any compromise in memory. The second achieves the first known attack of the GPS scheme in a time complexity of under 264 at the expense of some added memory requirements over the former.