A method for counting the number of polynomial equivalence classes

Journal of mathematical cryptology

article

Tianze Wang¹  Dongdai Lin¹ 

[1] State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences

关键词: Enumerative problem;    isomorphism of polynomials;    equivalence class;    multivariate public key cryptosystem;   

DOI  :  10.1515/jmc-2012-0017

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

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.

【 授权许可】

CC BY|CC BY-NC-ND