Finding Non-liner Register on Binary M-Sequence Generating Binary Multiplication Sequence

In the current time there is an important problem that is for a received linear or nonlinear binary sequence {zn} how we can find the nonlinear feedback shift register and its linear equivalent which generate this sequence. The linear orthogonal sequences, special M-Sequences, play a big role in these methods for solving this problem. In the current research trying give illuminations about the methods which are very useful for solving this problem under short sequences, and study these methods for finding the nonlinear feedback shift register of a multiplication sequence and its linear equivalent feedback shift register of a received multiplication binary sequence{zn} where the multiplication on h degrees of a binary linear sequence {an}, or finding the equivalent linear feedback shift register of {zn}, where the sequence {zn}of the form M-sequence, and these methods are very effectively. We can extend these methods for the large sequences using programming and modern computers with large memory

Метод построения нелинейного генератора двоичных последовательностей на сдвиговом регистре

Paper is dedicated to a problem of the design techniques of Nonlinear Feedback Shift Register (NFSR) with nonlinear feedback Boolean function, which ensure the repeat cycle 2n for n-bit register and improve the sequences quality characteristics which have an impact on data protection efficiency. The combinatorial method for obtaining nonlinear feedback functions which ensure the repeat cycle 2n for n-bit shift register has been worked out. It has been proved that proposed method allowed to increase the number of obtained feedback nonlinear function on one order in compare to known methods.Статья посвящена исследованию проблемы технологии проектирования сдвиговых регистров с нелинейными функциями обратной связи, которые гарантируют период повторения 2n для n-разрядного сдвигового регистра и обеспечивают улучшение характеристик двоичных последовательностей, которые важны для эффективности защиты информации. Разработан комбинаторный метод получения нелинейных булевых функций, обеспечивающий 2n для n-разрядного сдвигового регистра. Доказано, что предложенный метод позволяет на порядок увеличить количество нелинейных функций обратной связи по сравнению с известными методами

DEVELOPMENT OF THE SEARCH METHOD FOR NON-LINEAR SHIFT REGISTERS USING HARDWARE, IMPLEMENTED ON FIELD PROGRAMMABLE GATE ARRAYS

The nonlinear feedback shift registers of the second order inare considered, because based on them it can be developed a generator of stream ciphers with enhanced cryptographic strength. Feasibility of nonlinear feedback shift register search is analyzed. These registers form a maximal length sequence, using programmable logic devices. Performance evaluation of programmable logic devices in the generation of pseudo-random sequence by nonlinear feedback shift registers is given. Recommendations to increase this performance are given. The dependence of the maximum generation rate (clock frequency), programmable logic devices on the number of concurrent nonlinear registers is analyzed. A comparison of the generation rate of the sequences that are generated by nonlinear feedback shift registers is done using hardware and software. The author suggests, describes and explores the search method of nonlinear feedback shift registers, generating a sequence with a maximum period. As the main result are found non-linear 26, 27, 28 and 29 degrees polynomials

On cross joining de Bruijn sequences

We explain the origins of Boolean feedback functions of nonlinear feedback shift registers (NLFSRs) of fixed order n generating de Bruijn binary sequences. They all come into existence by cross joining operations starting from one maximum period feedback shift register, e.g., a linear one which always exists for any order n. The result obtained yields some constructions of NLFSRs generating maximum period $2^n-1$ binary sequences

Generating a Strong Key for a Stream Cipher Systems Based on Permutation Networks

The choice of binary Pseudonoise (PN) sequences with specific properties, having long period high complexity, randomness, minimum cross and auto- correlation which are essential for some communication systems. In this research a nonlinear PN generator is introduced . It consists of a combination of basic components like Linear Feedback Shift Register (LFSR), ?-element which is a type of RxR crossbar switches. The period and complexity of a sequence which are generated by the proposed generator are computed and the randomness properties of these sequences are measured by well-known randomness tests

Realizations of optimal signature analyzer

The realizations of optimal nonlinear signature analyzer are proposed. The analyzer is tuned for the testing sequence. The analyzer optimizes the number of signature sequences. It appears that this analyzer is essentially more effective in comparison with linear one. One of the practical realizations contains binary counter which is complicated device. Linear shift register with feedback is proposed to use instead of binary counter. Proposed circuit for nonlinear signature analyzer enable to reduce the number of sequences with equal signatures