Resistance of SNOW 2.0 Against Algebraic Attacks

SNOW 2.0, a software oriented stream cipher proposed by T. Johansson and P. Ekdahl in 2002 as an enhanced version of the NESSIE finalist SNOW 1.0, is usually considered as one of the strongest stream ciphers designed so far. This paper investigates the resistance of SNOW 2.0 against algebraic attacks. This is motivated by the fact that the main source of non-linearity in SNOW 2.0 comes from a permutation build upon the AES S-box, which inputs and outputs are well known to be related by numerous quadratic equations. We show that a slightly modified version of SNOW 2.0 is susceptible to an algebraic attack with time complexity about 2, and which requires no more than 1000 words of output. We then explore various ways to extend this attack to the actual stream cipher.