Attacking Bivium and Trivium with the characteristic set method

Abstract

In this paper we utilize an algebraic method called the characteristic set method to attack Bivium and Trivium in the guess-and-determine way. Our attack focuses on recovering the internal states of these two ciphers. We theoretically analyze the performance of different guessing strategies in the guess-and-determine method and present a good one. We show a large amount of experimental results about these two problems with different parameters. From these experimental data we obtain the following results. For Bivium, with 177-bit keystream the expected attack time by the characteristic set method is about 231.81 seconds. And for Trivium, with 288-bit keystream the expected attack time is about 2114.27 seconds. © 2011 Springer-Verlag.