Algebraic Cryptanalysis of A NLFSR Based Stream Cipher

Abstract

Among recent developments on stream ciphers, the algebraic attack has gained much attention. In this paper we concentrate on algebraic cryptanalysis of Grain, a non-linear feedback shift register (NLFSR) based stream cipher. The target here is to analyze generic key generating structure of Grain, that is why, we aim to recover the internal states of cipher rather than the key-bits. Experiments are carried out to solve these varying degree equations, with some guessed bits using Groebner basis technique. Our approach succeeds in recovering (approx) 1/2 of the internal stateAmong recent developments on stream ciphers, the algebraic attack has gained much attention. In this paper we concentrate on algebraic cryptanalysis of Grain, a non-linear feedback shift register (NLFSR) based stream cipher. The target here is to analyze generic key generating structure of Grain, that is why, we aim to recover the internal states of cipher rather than the key-bits. Experiments are carried out to solve these varying degree equations, with some guessed bits using Groebner basis technique. Our approach succeeds in recovering (approx) 1/2 of the internal state bits of Grain-1, while other half are guessed. While, in case of Grain-128, only 1/4 of the state bits can be obtained. bits of Grain-1, while other half are guessed. While, in case of Grain-128, only 1/4 of the state bits can be obtained.