Under Quantum Computer Attack: Is Rainbow a Replacement of RSA and Elliptic Curves on Hardware?

Abstract

Among cryptographic systems, multivariate signature is one of the most popular candidates since it has the potential to resist quantum computer attacks. Rainbow belongs to the multivariate signature, which can be viewed as a multilayer unbalanced OilVinegar system. In this paper, we present techniques to exploit Rainbow signature on hardware meeting the requirements of efficient high-performance applications. We propose a general architecture for efficient hardware implementations of Rainbow and enhance our design in three directions. First, we present a fast inversion based on binary trees. Second, we present an efficient multiplication based on compact construction in composite fields. Third, we present a parallel solving system of linear equations based on GaussJordan elimination. Via further other minor optimizations and by integrating the major improvement above, we implement our design in composite fields on standard cell CMOS Application Specific Integrated Circuits (ASICs). The experimental results show that our implementation takes 4.9 us and 242 clock cycles to generate a Rainbow signature with the frequency of 50 MHz. Comparison results show that our design is more efficient than the RSA and ECC implementations.

Feasibility Analysis of Cracking RSA with Improved Quantum Circuits of the Shor’s Algorithm

“…Te proposal of the RSA public key cryptosystem [1] has given rise to numerous scholarly discussions on this problem [2][3][4][5][6], in which security relies on the integer factorization. Te problem of integer factorization is to fnd a nontrivial factor of a given composite number.…”