Quantum Computing for Discrete Logarithms

Abstract

The Discrete Logarithm Problem (DLP) may be the first intractable computational number-theoretic problem to be considered for constructing cryptographic schemes by Diffie, Hellman and Merle at Stanford in 1976 and also by Ellis, Cocks and Williamson at the British GCHQ in 1970--1976. Today, DLP are widely used for constructing cryptographic systems and digital signatures, and the security of these systems depends heavily on the intractability of DLP. In this chapter, we discuss the quantum computing methods for solving the Discrete Logarithm Problem (DLP) and its extension Elliptic Curve Discrete Logarithm Problem (ECDLP).