Differential Cryptanalysis of T-Function Based Stream Cipher TSC-4

Abstract

Abstract. TSC-4 is a T-function based stream cipher with 80-bit key, and proposed as a candidate for ECRYPT eStream project. In this paper, we introduce a differential method to analyze TSC-4. Our attack is based on the vulnerable differential characteristics in the state initialization of TSC-4, and for the chosen IV pairs, the differential probability is up to 2 −15.40 in the case of weak keys. We show that there are about 2 72 weak keys among the total 2 80 keys. To recover 8 bits of a weak key needs about 2 40.53 chosen IV pairs. After that, we can search the other 72 key bits by an exhaustive attack.

Linear Relation on General Ergodic T-Function

“…The latter is out of scope of the paper; it worth noting here only that the ciphers were successfully attacked, however, using vulnerabilities other than the ones we indicate, see e.g. [33,40].…”

The formulas for the coefficients of the sum and product of p -adic integers with applications to Witt vectors

“…Thus, T-functions can be used in stream ciphers, block ciphers, pseudo-random number generators, hash functions, and so on. Recently, TSC-series stream ciphers ( [3], [4], [13]) which are based on T-functions were proposed by Hong et al as one of the candidates for the ECRYPT Stream Cipher project. As is well known, almost all of the applications require T-functions to have the single cycle property.…”