On tameness of Matsumoto-Imai central maps in three variables over the finite field $\mathbb F_2$

Abstract

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 F 2 is tame, and we describe the tame decompositions of the Matsumoto-Imai central maps.

Cryptographic Technology for Benefiting from Big Data

“…Our result is that we give the decomposition of some specific tame automorphisms which comprise the public key of an MPKC scheme. For more details of our security analysis, we refer the reader to [4,Main Theorem]. …”

Sign of Permutation Induced by Nagata Automorphism over Finite Fields

“…Multivariate polynomial cryptography is a potential candidate for post-quantum cryptography. One such example is the Tame Transformation Method (See, for example, (Chen & Moh, 2001), (Ding & Hodges, 2004), (Ding & Schmidt, 2004), (Goubin & Courtois, 2000), (Hakuta, Sato, & Takagi, 2016), (Hrdina, Kureš, & Vašík, 2010), (Moh, 1999), (Moh, 2003), (Moh, Chen, & Yang, 2004)). One of the building blocks for multivariate polynomial cryptography is a bijective polynomial map over F q .…”