Abstract:

This paper presents the application of a quantum algorithm called QBoolSol for solving fundamental problems in asymmetric cryp- tography: factorization, discrete logarithm, and elliptic curves discrete logarithm problems. The main idea is to transform each of these problems into a system of polynomial equations or optimization problems because all of them may be solved using the QBoolSol algorithm. Even though, the presented methods do not outperform Shor's algorithm. They are rather alternatives to it.