Total break of the SRP encryption scheme

Abstract

Multivariate Public Key Cryptography (MPKC) is one of the main candidates for secure communication in a post-quantum era. Recently, Yasuda and Sakurai proposed in [7] a new multivariate encryption scheme called SRP, which combines the Square encryption scheme with the Rainbow signature scheme and the Plus modifier. In this paper we propose a practical key recovery attack against the SRP scheme, which is based on the min-Q-rank property of the system. Our attack is very efficient and allows us to break the parameter sets recommended in [7] within minutes. Our attack shows that combining a weak scheme with a secure one does not automatically increase the security of the weak scheme.