SpongeMPH: A New Multivariate Polynomial Hash Function based on the Sponge Construction

The development of quantum computing has made a great challenge to traditional cryptography. Multivariate Quadratic Polynomial (MQ) problem serve as a basis of a potentially post-quantum cryptosystems. This paper proposes a new design of hash algorithm function called SpongeMPH (Hash Function Based on Multivariate Sponge), which constructed in a popular way, including domain extender using Sponge structure, whilst its internal permutation using multivariate polynomials. Comparing with the existing hash algorithms, the new hash algorithm has the following advantage: its security is base on a wide known mathematical problem; its hash output length can be changed easily.