Linear cryptanalysis of the TSC family of stream ciphers

Abstract

In this paper, we introduce a new cryptanalysis method for stream ciphers based on T-functions and apply it to the TSC family which was proposed by Hong et al.. Our attack are based on linear approximations of the algorithms (in particular of the T-function). Hence, it is related to correlation attack, a popular technique to break stream ciphers with a linear update, like those using LFSR's. We show a key-recovery attack for the two algorithms proposed at FSE 2005 : TSC-1 in 225.4 computation steps, and TSC-2 in 2 48.1 steps. The first attack has been implemented and takes about 4 minutes to recover the whole key on an average PC. Another algorithm in the family, called TSC-3, was proposed at the ECRYPT call for stream ciphers. Despite some differences with its predecessors, it can be broken by similar techniques. Our attack has complexity of 242 known keystream bits to distinguish it from random, and about 266 steps of computation to recover the full secret key. An extended version of this paper can be found on the ECRYPT website [23]. © International Association for Cryptologic Research 2005.