Efficient variant of Rainbow using sparse secret keys

Multivariate Public Key Cryptosystems (MPKC) is one of candidates for post-quantum cryptography. Rainbow is an MPKC digital signature scheme, with relatively efficient encryption and decryption processes. However, the size of the secret key of Rainbow is substantially larger than that of an RSA cryptosystem for the same security level. By using sparse secret keys, the size of the secret key of Rainbow can be reduced. In addition, a method using sparse secret keys can accelerate the signature generation of Rainbow. Matrix-based Rainbow and NT-Rainbow, which we previously proposed, are variants of Rainbow using sparse secret keys. These two variants of Rainbow reduce the size of the secret key of Rainbow, and improve the efficiency of the signature generation of Rainbow. In this paper, we combine these two variants of Rainbow. As a consequence, the combined scheme realizes even smaller size of the secret key and even more efficient signature generation than those of the two variants of Rainbow. In particular, in comparison with the original Rainbow, the secret key is reduced in size by about 76% and the signature generation is sped up by about 55% at the security level of 100 bits.