Efficient Key Generation for Rainbow

Abstract

Multivariate Cryptography is one of the main candidates for securing communication in a post-quantum world. One of the most promising schemes from this area is the Rainbow signature scheme. While this scheme provides very fast signature generation and verification, the key generation process of Rainbow is relatively slow. In this paper, we propose an algorithm which speeds up the key generation process of the standard Rainbow signature scheme by up to two orders of magnitude, such eliminating one of the few drawbacks of this scheme. Furthermore, we present an improved key generation algorithm for the CyclicRainbow signature scheme. This algorithm allows to generate a key pair for Cyclic Rainbow in essentially the same time as a key pair for standard Rainbow, thus making CyclicRainbow a practical alternative to the standard scheme. Our algorithms are implemented in the Rainbow proposal for the second round of the NIST standardization process for post-quantum cryptosystems.