In 2016, Yasuda et al. presented a new multivariate encryption technique based on the Square and Rainbow primitives and utilizing the plus modifier that they called SRP. The scheme achieved a smaller blow-up factor between the plaintext space and ciphertext space than most recent multivariate encryption proposals, but proved to be too aggressive and was completely broken by Perlner et al. in 2017. The scheme suffered from the same MinRank weakness that has allowed effective attacks on several notable big field multivariate schemes: HFE, multi-HFE, HFE-, for example.

We propose a related new encryption scheme retaining the desirable traits of SRP and patching its weaknesses. We call the scheme HFERP because it utilizes a similar construction as SRP with an HFE primitive replacing the Square polynomial. The effect of this substitution is to increase the Q-rank of the pubic key to such a degree that the MinRank attack is impossible. HFERP still retains the relatively small blow-up factor between the plaintext space and ciphertext space, and is thus a candidate for secure multivariate encryption without an essential doubling in size between plaintext and ciphertext.