Abstract.
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.
© 2013 by Walter de Gruyter Berlin Boston
This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
