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

Генераторы тестов для встроенного самотестирования дискретных устройств

Запропоновано новий метод синтезу генераторів детермінованих тестів для взбудованного самотестування дискретних пристроїв на основі зсувних регістрів з нелінійним зворотним зв'язком та перетворювачем тестових векторів.A new built-in test pattern generation method of precomputed test set is proposed. The pattern generator consists of two component : nonlinear feedback shift register generator and combinational logic to map the outputs of pattern generator

Comparison analysis of stream cipher algorithms for digital communication

The broadcast nature of radio communication such as in the HF (High Frequency) spectrum exposes the transmitted information to unauthorized third parties. Confidentiality is ensured by employing cipher system. For bulk transmission of data, stream ciphers are ideal choices over block ciphers due to faster implementation speed and not introducing error propagation. The stream cipher algorithms evaluated are based on the linear feedback shift register (LFSR) with nonlinear combining function. By using a common key length and worst case conditions, the strength of several stream cipher algorithms are evaluated using statistical tests, correlation attack, linear complexity profile and nonstandard test. The best algorithm is the one that exceeds all of the tests

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

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

Extended class of linear feedback shift registers

Shift registers with linear feedback are frequently used. They owe their popularity to very well developed theoretical base. Registers with feedback of prime polynomials are of particular practical importance. They are willingly applied as test sequence generators and test response compactors. The article presents an attempt to extend the class of registers with linear feedback. Basing on the formal description of the register, the algorithms of register transformation are proposed. It allows to obtain the registers with equivalent graphs.[1] I. Gosciniak, “Linear Registers with Mixed Feedback, in Polish; Rejestry liniowe z mieszanym sprzȩżeniem zwrotnym,” Pomiary Automatyka Kontrola, no. 1, pp. 4–6, 1996.[2] K. Iwasaki, “Analysis and proposal of signature circuits for LSI testing,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 7, no. 1, pp. 84–90, 1988.[3] L.-T. Wang, N. Touba, R. Brent, H. Xu, and H. Wang, “On Designing Transformed Linear Feedback Shift Registers with Minimum Hardware Cost – Technical Report,” Computer Engineering Research Center Department of Electrical & Computer Engineering The University of Texas at Austin, 2011.[4] J. Rajski, J. Tyszer, M. Kassab, and N. Mukherjee, “Method for Synthesizing Linear Finite State Machines,” U.S. Patent, No. 6,353,842, 2002.[5] I. Gosciniak, “Equivalent Form of Linear Feedback Shift Registers,” in XIXth National Conference Circuit Theory and Eletronic Networks, 1996, pp. 115–120.[6] L. Alaus, D. Noguet, and J. Palicot, “A Reconfigurable LFSR for Tristandard SDR Transceiver, Architecture and Complexity Analysis,” in Digital System Design Architectures, Methods and Tools, 2008. DSD ’08. 11th EUROMICRO Conference on. IEEE Computer Society, 2008, pp. 61–67.[7] R. Ash, Information Theory. John Wiley & Sons, 1967.[8] M. Kopec, “Can Nonlinear Compactors Be Better than Linear Ones?” IEEE Trans. Comput., no. 11, pp. 1275–1282, 1995.[9] A. Gucha and L. Kinney, “Relating the Cyclic Behaviour of Linear Intrainverted Feedback shift Registers,” IEEE Transactions on Computers, vol. 41, no. 9, pp. 1088–1100, 1992