Authors:
Xiaoyi Zhou
1
;
Jixin Ma
1
;
Wencai Du
2
;
Bo Zhao
3
;
Miltos Petridis
1
and
Yongzhe Zhao
4
Affiliations:
1
School of Computing and Mathematical Science, University of Greenwich, United Kingdom
;
2
School of Computer Science and Technology, Hainan University, China
;
3
College of Computer Science and Technology, Huazhong University of Science and Technology, China
;
4
College of Computer Science and Technology, Jilin University, China
Keyword(s):
Ergodic Matrix, Bisectional, Multivariate Quadratic, Fixing Variables, NP-hard.
Related
Ontology
Subjects/Areas/Topics:
Cryptographic Techniques and Key Management
;
Information and Systems Security
;
Public Key Crypto Applications
Abstract:
In this paper, we propose a multivariate quadratic (MQ) equation system based on ergodic matrix (EM) over a finite field with q elements (denoted as F^q). The system actually implicates a problem which is equivalent to the famous Graph Coloring problem, and therefore is NP complete for attackers. The complexity of bisectional multivariate quadratic equation (BMQE) system is determined by the number of the variables, of the equations and of the elements of F^q, which is denoted as n, m, and q, respectively. The paper shows that, if the number of the equations is larger or equal to twice the number of the variables, and qn is large enough, the system is complicated enough to prevent attacks from most of the existing attacking schemes.