A Systematic Construction of a -Module in TTM

Abstract

T. Moh invented the cryptosystem, Tame Transformation Method, abbreviated as TTM. Its encryption and decryption are very fast due to the general properties of tame automorphisms and small finite fields. The success of the system relies on the construction of the Q 8 -module. We give a systematic way to construct a Q m -module where m ¼ 2 k . This not only enhances the complexity and the security of TTM, but also makes TTM more accessible. Further discussion and generalization of this method are also given.

Cryptanalysis of an Implementation Scheme of the Tamed Transformation Method Cryptosystem

“…Recently, a family of versions of the functions Q 8 with much higher degrees was described in [2]. These again decompose into terms analogous to the S, T 1 and T 2 above and hence can be defeated by an analogous approach.…”

“…Goubin and Courtois claimed to have defeated this system in [3], but Chen and Moh refuted this claim in [1]. In this article, we use a completely different method to show that the implementation scheme suggested in [6] and also the ones suggested in [2] are not secure. Our approach is inspired by the work of Patarin on the Matsumoto-Imai scheme [7].…”

Cryptanalysis of the new TTS scheme in CHES 2004

“…The inventor of TTM refuted this claim in [1], and presented a new implementation scheme to support their case. In [7] another method was found to defeat the original TTM schemes in [15] and all other schemes suggested in [3]. Later Ding and Schmidt [8,9] also defeated the new schemes in [1], and pointed out that all existing TTM schemes share a common defect that makes them insecure.…”

Cryptanalysis of an Implementation of TTM Cryptosystems Based on Q2k -module

“…The success of this system relies on the construction of Q 8 -type modules. Some constructions of Q k -module are known, such as the systematic way to construct Q 2 k -module proposed by Chou et al [7].…”