Poluianenko M. Models and methods of synthesis of nonlinear feedback shift registers for the scheme of the symmetric key algorithm

The dissertation solves scientific task - developing and theoretical substantiation of method for synthesis nonlinear feedback shift registers with given length and given constructive characteristics for their use in the scheme of the symmetric-key algorithm. The main goal of the work is decreasing computation complexity of synthesis nonlinear feedback shift registers with given length that satisfies given requirements of encryption protection for their use in the scheme of the symmetric-key algorithm. In this paper, the method for synthesis nonlinear feedback shift registers of the order two was improved. This method substantiates necessary conditions for forming of maximum length pseudorandom sequences. This method differs from other methods in that it uses developed mathematical model with simplified formalized description of nonlinear feedback of the second order, it allows to significantly reduce computation complexity of the synthesis process. The new method for synthesis nonlinear feedback shift registers with maximum length sequences was created in the work; the method differs from existing methods for selection search in that it has lower computation complexity and allows to find big nonlinear shift registers with given constructive characteristics. It has been created algorithm for search for nonlinear feedback shift registers with the help of the developed software and hardware means that form of maximum length sequences for up to 32 cells. The model of evaluation of cryptographic stability of scheme of the symmetric-key algorithm is further developed. According this model systems of criteria and indicators of stability of the pseudorandom sequence formed by nonlinear feedback shift registers were created. Those studies allow to analyze of rate of protection of nonlinear feedback shift registers in compare with linear feedback shift registers against of widespread cryptographic attacks. Advantages of using constructions of nonlinear feedback shift registers in stream cipher systems are substantiate. The obtained practical results are as follows. The new method for synthesis of nonlinear feedback shift registers of the second order with maximal forming sequence length and given constructive characteristics is obtained. Those practical results allow to decrease computation complexity of search methods and procedures of synthesis nonlinear feedback shift registers. Software and hardware complex for synthesis nonlinear feedback shift registers with given constructive characteristics and length has been developed. The hardware part use programmable logic device with help of computing power of CPU and GPU. The recommendations for it use are given. A system of evaluation of analytical and empirical stability of the nonlinear feedback shift registers of the second order in the process of developing the scheme of the symmetric-key algorithm was obtained, experimentally verified and implemented. Special mathematical, hardware and software means have been developed. Those means are used for experimental study of the properties of pseudorandom sequences that generated by nonlinear shift registers.