Guess and Determine Attack on Bivium

Bivium is a simplified version of Trivium, a hardware profile finalist of the eSTREAM project. Bivium has an internal state size of 177 bits and a key length of 80 bits. In this paper, a guess and determine attack on this cipher is introduced. In the proposed method, the best linear approximations for the updating functions are first defined. Then by using these calculated approximations, a system of linear equations is built. By guessing 30 bits of internal state, the system is solved and all the other 147 remaining bits are determined. The complexity of the attack is O (2), which is an improvement to the previous guess and determine attack with a complexity of order O(2). Keywords—Bivium, Guess and Determine Attack, Stream Ciphers, Linear Approximations, Entropy