Triangular transformation method (TTM) is one of the multivariate public key cryptosystems (MPKC) based on the intractability of tame decomposition problem. In TTM, a special class of tame automorphisms are used to construct encryption schemes. However, because of the specificity of such tame automorphisms, it is important to evaluate the computational complexity of the tame decomposition problem for secure use of MPKC. In this paper, as the first step for security evaluations, we focus on Matsumoto-Imai cryptosystems. We shall prove that the Matsumoto-Imai central maps in three variables over F2 is tame, and we describe the tame decompositions of the Matsumoto-Imai central maps.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Computer Networks and Communications
- Discrete Mathematics and Combinatorics
- Applied Mathematics