Circulant Rainbow: A New Rainbow Variant With Shorter Private Key and Faster Signature Generation

Abstract

Rainbow is one of the most important signature schemes in multivariate public key cryptography. It enjoys a strong security guarantee and is a promising signature scheme in Post-Quantum Cryptography. However, it suffers from large key size. In this paper, we propose Circulant Rainbow with shorter private key and higher signing efficiency. In Circulant Rainbow, we introduce rotating relations into parts of Rainbow private key to speed up the signing procedure and reduce the private key size. We carefully choose security parameters so that our Circulant Rainbow is secure against all known attacks. In our experiment, Circulant Rainbow is about three times faster than original Rainbow and it can reduce the private key size by about 45%. We also make a comparison of Circulant Rainbow with some traditional signature schemes, the results show that Circulant Rainbow is a promising candidate in Post-Quantum Cryptography.