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

Cyclostationary Random Number Sequences for the Tsetlin Machine

Author's accepted manuscriptThe Tsetlin Machine (TM) constitutes an emerging machine learning algorithm that has shown competitive performance on several benchmarks. The underlying concept of the TM is propositional logic determined by a group of finite state machines that learns patterns. Thus, TM-based systems naturally lend themselves to low-power operation when implemented in hardware for micro-edge Internet-of-Things applications. An important aspect of the learning phase of TMs is stochasticity. For low-power integrated circuit implementations the random number generation must be carried out efficiently. In this paper, we explore the application of pre-generated cyclostationary random number sequences for TMs. Through experiments on two machine learning problems, i.e., Binary Iris and Noisy XOR, we demonstrate that the accuracy is on par with standard TM. We show that through exploratory simulations the required length of the sequences that meets the conflicting tradeoffs can be suitably identified. Furthermore, the TMs achieve robust performance against reduced resolution of the random numbers. Finally, we show that maximum-length sequences implemented by linear feedback shift registers are suitable for generating the required random numbers.acceptedVersio

High Speed and Low Power Pseudo Noise(PN) Sequence Generator

The Pseudo Noise (PN) sequence has become a significant component in digital communication. A pseudo random code are generated using two techniques namely, gold code and Kasami code. The generation of PN sequence involves the use of Linear Feedback Shift Register (LFSR) as its building block. When compared to other multiplexing methods,gold code and Kasami code techniques are better in terms of power utilization, noise flexibility and frequency efficiency. The generation of these codes involves the use of two maximum length sequence (M-sequence). The auto-correlation properties of gold and Kasami sequences are the basis for this research work. The software used to simulate these methods is NC Launchand the language used is Verilog Hardware Description Language(HDL). The results of the above two methods are compared in terms of power utilization and speed in the CADENCE environment. When comparing Gold code with Kasami code, Gold code consumes 42% less power than the Kasami code. In the modified Kasami code generator, the speed is increased by 8%, when compared to modified Gold code generator

A transformation sequencing approach to pseudorandom number generation

This paper presents a new approach to designing pseudorandom number generators based on cellular automata. Current cellular automata designs either focus on i) ensuring desirable sequence properties such as maximum length period, balanced distribution of bits and uniform distribution of n-bit tuples etc. or ii) ensuring the generated sequences pass stringent randomness tests. In this work, important design patterns are first identified from the latter approach and then incorporated into cellular automata such that the desirable sequence properties are preserved like in the former approach. Preliminary experiment results show that the new cellular automata designed have potential in passing all DIEHARD tests

Layered cellular automata for pseudorandom number generation

The proposed Layered Cellular Automata (L-LCA), which comprises of a main CA with L additional layers of memory registers, has simple local interconnections and high operating speed. The time-varying L-LCA transformation at each clock can be reduced to a single transformation in the set formed by the transformation matrix of a maximum length Cellular Automata (CA), and the entire transformation sequence for a single period can be obtained. The analysis for the period characteristics of state sequences is simplified by analyzing representative transformation sequences determined by the phase difference between the initial states for each layer. The L-LCA model can be extended by adding more layers of memory or through the use of a larger main CA based on widely available maximum length CA. Several L-LCA (L=1,2,3,4) with 10- to 48-bit main CA are subjected to the DIEHARD test suite and better results are obtained over other CA designs reported in the literature. The experiments are repeated using the well-known nonlinear functions and in place of the linear function used in the L-LCA. Linear complexity is significantly increased when or is used

Permutation and sampling with maximum length CA for pseudorandom number generation

In this paper, we study the effect of dynamic permutation and sampling on the randomness quality of sequences generated by cellular automata (CA). Dynamic permutation and sampling have not been explored in previous CA work and a suitable implementation is shown using a two CA model. Three different schemes that incorporate these two operations are suggested - Weighted Permutation Vector Sampling with Controlled Multiplexing, Weighted Permutation Vector Sampling with Irregular Decimation and Permutation Programmed CA Sampling. The experiment results show that the resulting sequences have varying degrees of improvement in DIEHARD results and linear complexity compared to the CA

Pseudorandom number generation with self programmable cellular automata

In this paper, we propose a new class of cellular automata – self programming cellular automata (SPCA) with specific application to pseudorandom number generation. By changing a cell's state transition rules in relation to factors such as its neighboring cell's states, behavioral complexity can be increased and utilized. Interplay between the state transition neighborhood and rule selection neighborhood leads to a new composite neighborhood and state transition rule that is the linear combination of two different mappings with different temporal dependencies. It is proved that when the transitional matrices for both the state transition and rule selection neighborhood are non-singular, SPCA will not exhibit non-group behavior. Good performance can be obtained using simple neighborhoods with certain CA length, transition rules etc. Certain configurations of SPCA pass all DIEHARD and ENT tests with an implementation cost lower than current reported work. Output sampling methods are also suggested to improve output efficiency by sampling the outputs of the new rule selection neighborhoods

A Comparative Study of Some Pseudorandom Number Generators

We present results of an extensive test program of a group of pseudorandom number generators which are commonly used in the applications of physics, in particular in Monte Carlo simulations. The generators include public domain programs, manufacturer installed routines and a random number sequence produced from physical noise. We start by traditional statistical tests, followed by detailed bit level and visual tests. The computational speed of various algorithms is also scrutinized. Our results allow direct comparisons between the properties of different generators, as well as an assessment of the efficiency of the various test methods. This information provides the best available criterion to choose the best possible generator for a given problem. However, in light of recent problems reported with some of these generators, we also discuss the importance of developing more refined physical tests to find possible correlations not revealed by the present test methods.Comment: University of Helsinki preprint HU-TFT-93-22 (minor changes in Tables 2 and 7, and in the text, correspondingly