Proxy Signature Scheme Based on Isomorphisms of Polynomials

The proxy signatures are important cryptosystems that are widely adopted in different applications. Most of the proxy signature schemes so far are based on the hardness of integer factoring, discrete logarithm, and/or elliptic curve. However, Shor proved that the emerging quantum computers can solve the problem of prime factorization and discrete logarithm in polynomial-time, which threatens the security of current RSA, ElGamal, ECC, and the proxy signature schemes based on these problems. We propose a novel proxy signature scheme based on the problem of Isomorphism of Polynomials (IP) which belongs to a major category of Multivariate Public Key Cryptography (MPKC). Through security discussion, our scheme can reach the same security level as the signature scheme based on IP problem. The most attractive advantage of our scheme should be its feature to potentially resist the future quantum computing attacks. Our scheme also owns some important properties of proxy signature schemes, such as strong unforgeability, strong identifiability, strong undeniability, secret-key's dependence, distinguishability, etc. The scheme is implemented in C/C++ programming language, and the performance shows that the scheme is efficient. The parameters we choose can let security level of the scheme up to 286.59.