Global Linear Complexity Analysis of Filter Keystream Generators

An efficient algorithm for computing lower bounds on the global linear complexity of nonlinearly filtered PN-sequences is presented. The technique here developed is based exclusively on the realization of bit wise logic operations, which makes it appropriate for both software simulation and hardware implementation. The present algorithm can be applied to any arbitrary nonlinear function with a unique term of maximum order. Thus, the extent of its application for different types of filter generators is quite broad. Furthermore, emphasis is on the large lower bounds obtained that confirm the exponential growth of the global linear complexity for the class of nonlinearly filtered 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

Complexity analysis of binary nonlinear feedforward sequences through minimum polynomials of compound matrices

AbstractThe problem of finding the complexity of the Nonlinear feedforward sequences has been analysed and a unified method has been developed for finding the complexity of such sequences for the cases when feedback is 1.(i) an irreducible polynomial;2.(ii) product of two irreducible polynomials;3.(iii) power of an irreducible polynomial. The method is based on the minimum polynomial of the compound matrix formed from the companion matrix of the feedback polynomial. Apart from being a unified method, this approach has the advantage that it can be applied to any level of logic and one can get the minimal generator of all possible non-linear feedforward 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

Метод та програмні засоби тестування генераторів псевдовипадкових послідовностей для систем захисту інформації

Дипломний проект присвячено вирішенню задачі підвищення ефективності оцінки якості псевдовипадкових двійкових послідовностей, що використовуються в засобах криптографічного захисту даних і, зокрема в потокових шифрах. В рамках дипломного проекту досліджено та практично реалізовано підхід до підвищення достовірності оцінки непередбачуваності псевдовипадкових двійкових послідовностей на основі дослідження властивостей нелінійних відтворюючих моделей. Розроблено алгоритм побудови нелінійної відтворюючої моделі та програмні засоби, які реалізують запропонований алгоритм. Теоретично та експериментально доведено, що використання розробленої технології оцінки непередбачуваності псевдовипадкових двійкових послідовностей, що використовуються в засобах криптографічного захисту даних дозволяє зменшити обчислювальну складність в порівнянні з відомими методами, а значить, прискорити процес тестування або збільшити його надійність за рахунок тестування в межах визначених часових ресурсів більш довгих послідовностей.The diploma project is devoted to solving the problem of improving the efficiency of quality assessment of pseudo - random binary sequences used in cryptographic data protection and, in particular, in streaming ciphers. Within the framework of the diploma project the approach to increase of reliability of an estimation of unpredictability of pseudorandom binary sequences on the basis of research of properties of nonlinear reproducing models is investigated and practically realized. An algorithm for constructing a nonlinear reproduction model and software that implements the proposed algorithm have been developed. It is theoretically and experimentally proved that the use of the developed technology for estimating the unpredictability of pseudo-random binary sequences used in cryptographic data protection means allows to reduce computational complexity compared to known methods, and thus speed up the testing process or increase its reliability by testing time limits of longer sequences

Mathematical and algorithmic methods for finding disjoint Rosa-type sequences

A Rosa sequence of order n is a sequence S = (s1; s2; ..., s2n+1) of 2n + 1 integers satisfying the conditions: (1) for every k ∈ {1; 2;...; n} there are exactly two elements sᵢ; sj ∈ S such that si = sj = k; (2) if sᵢ = sj = k; i < j, then j - i = k; and (3) sn+1 = 0 (sn+1 is called the hook). Two Rosa sequences S and S' are disjoint if sᵢ = sj = k = s't = s'ᵤ implies that {i;j} ≠ {t,u}, for all k = 1;..., n. In 2014, Linek, Mor, and Shalaby [18] introduced several new constructions for Skolem, hooked Skolem, and Rosa rectangles. In this thesis, we gave new constructions for four mutually disjoint hooked Rosa sequences and we used them to generate cyclic triple systems CTS₄(v). We also obtained new constructions for two disjoint m-fold Skolem sequences, two disjoint m-fold Rosa sequences, and two disjoint indecomposable 2-fold Rosa sequences of order n. Again, we can use these sequences to construct cyclic 2-fold 3-group divisible design 3-GDD and disjoint cyclically indecomposable CTS₄(6n+3). Finally, we introduced exhaustive search algorithms to find all distinct hooked Rosa sequences, as well as maximal and maximum disjoint subsets of (hooked) Rosa sequences

Small-world interconnection networks for large parallel computer systems

The use of small-world graphs as interconnection networks of multicomputers is proposed and analysed in this work. Small-world interconnection networks are constructed by adding (or modifying) edges to an underlying local graph. Graphs with a rich local structure but with a large diameter are shown to be the most suitable candidates for the underlying graph. Generation models based on random and deterministic wiring processes are proposed and analysed. For the random case basic properties such as degree, diameter, average length and bisection width are analysed, and the results show that a fast transition from a large diameter to a small diameter is experienced when the number of new edges introduced is increased. Random traffic analysis on these networks is undertaken, and it is shown that although the average latency experiences a similar reduction, networks with a small number of shortcuts have a tendency to saturate as most of the traffic flows through a small number of links. An analysis of the congestion of the networks corroborates this result and provides away of estimating the minimum number of shortcuts required to avoid saturation. To overcome these problems deterministic wiring is proposed and analysed. A Linear Feedback Shift Register is used to introduce shortcuts in the LFSR graphs. A simple routing algorithm has been constructed for the LFSR and extended with a greedy local optimisation technique. It has been shown that a small search depth gives good results and is less costly to implement than a full shortest path algorithm. The Hilbert graph on the other hand provides some additional characteristics, such as support for incremental expansion, efficient layout in two dimensional space (using two layers), and a small fixed degree of four. Small-world hypergraphs have also been studied. In particular incomplete hypermeshes have been introduced and analysed and it has been shown that they outperform the complete traditional implementations under a constant pinout argument. Since it has been shown that complete hypermeshes outperform the mesh, the torus, low dimensional m-ary d-cubes (with and without bypass channels), and multi-stage interconnection networks (when realistic decision times are accounted for and with a constant pinout), it follows that incomplete hypermeshes outperform them as well