scholarly journals Generalized Galois-Fibonacci Matrix Generators Pseudo-Random Sequences

2021 ◽  
Vol 13 (6) ◽  
pp. 57-69
Author(s):  
Anatoly Beletsk ◽  
Keyword(s):  
Irreducible Polynomial ◽  
Galois Field ◽  
Linear Feedback ◽  
Random Numbers ◽  
Unknown Parameters ◽  
Linear Feedback Shift Registers ◽  
The Matrix ◽  
Generalized Matrix ◽  
Bm Algorithm ◽  
Fibonacci Matrix

The article discusses various options for constructing binary generators of pseudo-random numbers (PRN) based on the so-called generalized Galois and Fibonacci matrices. The terms "Galois matrix" and "Fibonacci matrix" are borrowed from the theory of cryptography, in which the linear feedback shift registers (LFSR) generators of the PRN according to the Galois and Fibonacci schemes are widely used. The matrix generators generate identical PRN sequences as the LFSR generators. The transition from classical to generalized matrix PRN generators (PRNG) is accompanied by expanding the variety of generators, leading to a significant increase in their cryptographic resistance. This effect is achieved both due to the rise in the number of elements forming matrices and because generalized matrices are synthesized based on primitive generating polynomials and polynomials that are not necessarily primitive. Classical LFSR generators of PRN (and their matrix equivalents) have a significant drawback: they are susceptible to Berlekamp-Messi (BM) attacks. Generalized matrix PRNG is free from BM attack. The last property is a consequence of such a feature of the BM algorithm. This algorithm for cracking classical LFSR generators of PRN solves the problem of calculating the only unknown – a primitive polynomial generating the generator. For variants of generalized matrix PRNG, it becomes necessary to determine two unknown parameters: both an irreducible polynomial and a forming element that produces a generalized matrix. This problem turns out to be unsolvable for the BM algorithm since it is designed to calculate only one unknown parameter. The research results are generalized for solving PRNG problems over a Galois field of odd characteristics.

scholarly journals Introduction to Stochastic Computing using a Remote Lab with Reconfigurable Logic

2016 ◽  
Vol 12 (04) ◽  
pp. 23
Author(s):  
Jorge Lobo
Keyword(s):  
Random Number ◽  
Random Number Generation ◽  
Linear Feedback ◽  
Short Paper ◽  
Integration Time ◽  
Random Numbers ◽  
Reconfigurable Logic ◽  
Linear Feedback Shift Registers ◽  
Stochastic Computing ◽  
Remote Lab

This short paper introduces the basic concepts of Stochastic Computing (SC), and presents additions to a remote lab with reconfigurable logic to allow testing SC circuits. Recently, SC has been revisited and evaluated as a possible way of performing approximate probabilistic computations for artificial perception systems. New modules allow the generation of pseudo-random numbers, given a seed key and using linear feedback shift registers, but also having true random number generation using ring oscillators and embedded PLLs. Stochastic computing allows a tradeoff between resource usage and precision, allowing very simple circuits to perform computations, at the expense of a longer integration time to have reasonable results. We provide the basic stochastic computing modules, so that any user can use them to build a stochastic computing circuit and go beyond software simulations, providing a remote hardware device to test real circuits at high clock speeds.

scholarly journals What Causes to Tune a Condition of Exactly Identical Fault-Masks Behaviors in an LFSR based BIST Methodology

2017 ◽  
Vol 10 (04) ◽  
pp. 710-717
Author(s):  
A. Ahmad ◽  
D. Al Abri ◽  
S. S. Al Busaidi ◽  
M. M. Bait-Suwailam
Keyword(s):  
Linear Feedback ◽  
Test Sequence ◽  
Linear Feedback Shift Registers ◽  
Random Test ◽  
Signature Analyzer ◽  
Simulation Results ◽  
Feedback Shift Registers ◽  
Self Test ◽  
Sequence Generator ◽  
Feedback Connections

The authors show that in a Built-In Self-Test (BIST) technique, based on linear-feedback shift registers, when the feedback connections in pseudo-random test-sequence generator and signature analyzer are images of each other and corresponds to primitive characteristic polynomial then behaviors of faults masking remains identical. The simulation results of single stuck-at faults show how the use of such feedback connections in pseudo-random test-sequence generator and signature analyzer yields to mask the same faults.

scholarly journals ВДОСКОНАЛЕНА ПОЛІНОМІАЛЬНО-СКЛАДНА АТАКА ВІДНОВЛЕННЯ ВІДКРИТОГО ТЕКСТУ НА РАНЦЕВИЙ ШИФР НА ОСНОВІ МАТРИЦЬ

2020 ◽  
pp. 67-74
Author(s):  
Олексій Сергійович Вамболь
Keyword(s):  
Discrete Logarithm ◽  
Public Information ◽  
Galois Field ◽  
Secret Key ◽  
The Matrix ◽  
Encryption Schemes ◽  
Shared Secret ◽  
Symmetric Key ◽  
Asymmetric Encryption ◽  
The Given

Asymmetric ciphers are widely used to ensure the confidentiality of data transmission via insecure channels. These cryptosystems allow the interacting parties to create a shared secret key for a symmetric cipher in such a way that an eavesdropper gets no information useful for cryptanalysis. Network security protocols that use asymmetric ciphers include TLS, S/MIME, OpenPGP, Tor, and many others. Some of the asymmetric encryption schemes are homomorphic, that is, that they allow calculations on encrypted data to be performed without preliminary decryption. The aforesaid property makes possible using these cryptosystems not only for symmetric key establishment but also in several areas of application, in particular in secret voting protocols and cloud computing. The matrix-based knapsack cipher is a new additively homomorphic asymmetric encryption scheme, which is based on the properties of isomorphic transformations of the inner direct product of diagonal subgroups of a general linear group over a Galois field. Unlike classic knapsack encryption schemes, the cryptographic strength of this cipher depends on the computational complexity of the multidimensional discrete logarithm problem. Despite some useful properties, further research into the cryptographic strength of the matrix-based knapsack cipher has found serious drawbacks inherent in this cryptographic scheme. In the given paper an improved polynomial-time plaintext-recovery attack on the matrix-based knapsack cipher is proposed. Applying this cryptanalytic method requires only public information and has time complexity O(t1.34), where t denotes the decryption time of the attacked cryptosystem. The aforementioned attack is more productive and easier to implement in software in comparison with the original one. The advantages of the proposed method are due to using in its algorithm the simple and relatively fast matrix trace operation instead of more complex and slower transformations.

scholarly journals THE GENERALIZED MATRIX VALUED HYPERGEOMETRIC EQUATION

2010 ◽  
Vol 21 (02) ◽  
pp. 145-155 ◽  
Author(s):  
P. ROMÁN ◽  
S. SIMONDI
Keyword(s):  
Differential Equation ◽  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Hypergeometric Functions ◽  
Spherical Functions ◽  
Hypergeometric Equation ◽  
Necessary Condition ◽  
Hypergeometric Differential Equation ◽  
The Matrix ◽  
Generalized Matrix

The matrix valued analog of the Euler's hypergeometric differential equation was introduced by Tirao in [4]. This equation arises in the study of matrix valued spherical functions and in the theory of matrix valued orthogonal polynomials. The goal of this paper is to extend naturally the number of parameters of Tirao's equation in order to get a generalized matrix valued hypergeometric equation. We take advantage of the tools and strategies developed in [4] to identify the corresponding matrix hypergeometric functions nFm. We prove that, if n = m + 1, these functions are analytic for |z| < 1 and we give a necessary condition for the convergence on the unit circle |z| = 1.

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