Toward real-life implementation of signature schemes from the strong RSA assumption

Abstract

This paper introduces our work on performance improvement of signature schemes based on the strong RSA assumption for the purpose of real-life implementation and deployment. Many signature schemes based on the strong RSA assumption have been proposed in literature. The main advantage of these schemes is that they have security proofs in the standard model, while the traditional RSA scheme can only be demonstrated secure in the Random Oracle Model. However, the downside is the loss of efficiency among these schemes. Almost all these schemes double the computational cost of signature generation in the RSA scheme. So far the research in this area is more focusing on theoretical aspect. In this paper, we introduce techniques which greatly improve the performance of available schemes, and obtain a state-of-the-art signature scheme in the strong RSA family. In a typical setting where the RSA modulus is 1024 bits, it needs only one exponentiation calculation at the cost of about 160 modular multiplications, and a 162-bit prime number generation. This cost is even lower than the RSA signature scheme. Our work brings the current theoretical results into real-life implementation and deployment. © 2012 Springer-Verlag.