Using SAT Solvers to Finding Short Cycles in Cryptographic Algorithms

A desirable property of iterated cryptographic algorithms, such as stream ciphers or pseudo-random generators, is the lack short cycles. Many previously mentioned algorithms are based on use linear feedback shift registers (LFSR) and nonlinear (NLFSR) their combination. It currently known how to construct LFSR generate a bit sequence with maximum period, but there no knowledge in case NLFSR. The latter would be useful cryptography application (to have few taps relatively low algebraic degree). In this article, we propose simple method generation equations describe find solutions using an SAT solver exclude cycles register (NLFSR). Thanks AIG graphs, it also possible fully automate our algorithm, results its operation comparable obtained by manual equations. We present experiments which successfully found NLFSRs used KSG, Grain-80, Grain-128 Grain-128a Bivium Trivium (without constants initialization step).