A method for counting the number of polynomial equivalence classes

As one of the most fundamental problems in multivariate public key cryptosystems (MPKC), Isomorphism of Polynomial (IP) induces an equivalence relation on the polynomials systems. The enumeration problem associated to IP consists of counting the number of equivalence classes and the cardinality of each class. The two problems correspond exactly to the study of the total number of different cryptographic schemes and the size of “equivalent keys”. In this paper we give an algorithm using a divide-and-conquer method to count the number of equivalence classes according to the linear equivalence relation induced by the IP1S problem when . Then by giving the complexity gain of this algorithm compared with the exhaustive search algorithm and the experimental results, we show the high efficiency of this new algorithm