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

Abstract

-TTM cryptosystems proposed by T.Moh are very fast due to the properties of tame automorphisms and small finite fields. The success of the first implementation of this system relies on the construction of Q 8 -module. Unfortunately, Jintai Ding and Timonthy Hodges have defeated it by decomposing function Q 8 into terms S, T 1 , T 2 . Later Chunyen Chou, D. J. Guan and Jiunming Chen gave a systematic way to construct Q 2 k -module. In this paper, we describe an implementation of TTM cryptosystems based on this Q 2 k -module, then with method similar to Ding-Hodges, we break this implementation. For any given ciphertext, we can derive the corresponding plaintext within O((n+r) 6 ) F 2 m -operations, where n+r is the number of ciphertext variables.Index Terms -Multivariate public key cryptosystems, TTM, high order linearization equations.