Conditional Differential Cryptanalysis of NLFSR-Based Cryptosystems

Non-linear feedback shift registers are widely used in lightweight cryptographic primitives. For such constructions we propose a general analysis technique based on differential cryptanalysis. The essential idea is to identify conditions on the internal state to obtain a deterministic differential characteristic for a large number of rounds. Depending on whether these conditions involve public variables only, or also key variables, we derive distinguishing and partial key recovery attacks. We apply these methods to analyse the security of the eSTREAM finalist Grain v1 as well as the block cipher family KATAN/KTANTAN. This allows us to distinguish Grain v1 reduced to 104 of its 160 rounds and to recover some information on the key. The technique naturally extends to higher order differentials and enables us to distinguish Grain-128 up to 215 of its 256 rounds and to recover parts of the key up to 213 rounds. All results are the best known thus far and are achieved by experiments in practical time.