An Efficient Signature Scheme based on Factoring and Discrete Logarithm

TL;DR

This paper introduces a new cryptographic signature scheme that combines the hardness of factoring and discrete logarithm problems, offering an efficient and secure method based on these well-known hard problems.

Contribution

It presents a novel signature scheme that leverages both the cube root extraction and discrete logarithm problems, enhancing security and efficiency.

Findings

The scheme is strongly secure assuming the hardness of IFP and DLP.

Key generation is simple and based on discrete logarithms.

Signature computation involves cube root and DLP operations, which are efficient.

Abstract

This paper proposes a new signature scheme based on two hard problems : the cube root extraction modulo a composite moduli (which is equivalent to the factorisation of the moduli, IFP) and the discrete logarithm problem(DLP). By combining these two cryptographic assumptions, we introduce an efficient and strongly secure signature scheme. We show that if an adversary can break the new scheme with an algorithm $\mathcal{A},$ then $\mathcal{A}$ can be used to sove both the DLP and the IFP. The key generation is a simple operation based on the discrete logarithm modulo a composite moduli. The signature phase is based both on the cube root computation and the DLP. These operations are computationally efficient.