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Security and Communication Networks
Volume 2018 (2018), Article ID 2369507, 9 pages
Research Article

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

School of Computer Engineering, Shenzhen Polytechnic, Shenzhen 518055, China

Correspondence should be addressed to Haibo Yi

Received 26 October 2017; Accepted 15 January 2018; Published 11 February 2018

Academic Editor: Umar M. Khokhar

Copyright © 2018 Haibo Yi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 Oil-Vinegar 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 Gauss-Jordan 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  us and clock cycles to generate a Rainbow signature with the frequency of  MHz. Comparison results show that our design is more efficient than the RSA and ECC implementations.