Linear Sequential Circuit Approximation of Grain and Trivium Stream Ciphers

Grain and Trivium are two hardware oriented synchronous stream ciphers proposed as the simplest candidates to the ECRYPT Stream Cipher Project, both dealing with 80-bit secret keys. In this paper we apply the linear sequential circuit approximation method to evaluate the strength of these stream ciphers against distinguishing attack. In this approximation method which was initially introduced by Golic in 1994, linear models are effectively determined for autonomous finite-state machines. We derive linear functions of consecutive key-stream bits which are held with correlation coefficient of about 2 and 2 for Grain and Trivium ciphers, respectively. Then using the concept of socalled generating function, we turn them into linear functions with correlation coefficient of 2 for Grain and 2 for Trivium. It shows that the Grain output sequence can be distinguished from a purely random sequence, using about 2 bits of the output sequence with the same time complexity. However, our attempt fails to find a successful distinguisher for Trivium.