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Transition Fault Testability in Bit Parallel Multipliers over GF(2^{m})

H. Rahaman, J. Mathew, B.K. Sikdar, D.K. Pradhan
2007 Proceedings of the ... IEEE VLSI Test Symposium  
In this article, a C-testable design for detecting transition faults in the polynomial basis (PB) bit parallel (BP) multiplier circuits over GF(2 m ) is discussed.  ...  As the GF(2 m ) multipliers have found critical applications in public key cryptography and need secure internal testing, a Built-in Self-Test (BIST) circuit may be used for generating test patterns internally  ...  Each element A∈ GF(2 m ) can be expressed with respect to the PB as a polynomial of degree (m-1) over GF (2) , i.e. ∑ − = = 1 0 ) ( m i i i x a x A where a i ∈ GF (2) .  ... 
doi:10.1109/vts.2007.83 dblp:conf/vts/RahamanMSP07 fatcat:yrpiygeflvhorgcniejegctavq

$\textrm{GF}(2^m)$ Finite-Field Multipliers with Reduced Activity Variations [chapter]

Danuta Pamula, Arnaud Tisserand
2012 Lecture Notes in Computer Science  
In this work, we present GF(2 m ) multipliers with reduced activity variations for asymmetric cryptography. Useful activity of typical multiplication algorithms is evaluated.  ...  We propose modified multiplication algorithms and multiplier architectures to reduce useful activity variations during an operation.  ...  We have considered GF(2 m ) elements represented by polynomial basis of the form {1, x, x 2 , ..., x m−2 , x m−1 }.  ... 
doi:10.1007/978-3-642-31662-3_11 fatcat:bxdr7zzfgfafliluucqwn7qiee

Modelling nonlinear sequence generators in terms of linear cellular automata

Amparo Fúster-Sabater, Dolores de la Guía-Martínez
2007 Applied Mathematical Modelling  
The linearity of these cellular models can be advantageously used in two different ways: (a) for the analysis and/or cryptanalysis of the CCSGs and (b) for the reconstruction of the output sequence obtained  ...  In this work, a wide family of LFSR-based sequence generators, the so-called Clock-Controlled Shrinking Generators (CCSGs), has been analyzed and identified with a subset of linear Cellular Automata (CA  ...  Such an algorithm takes as input an irreducible polynomial Q(x) ∈ GF (2)[x] defined over a finite field and computes two reversal linear CA whose output sequences have Q(x) as characteristic polynomial  ... 
doi:10.1016/j.apm.2005.08.013 fatcat:u6hwyco5frfvrhjgeh2vvrvpa4

A Reconfigurable System on Chip Implementation for Elliptic Curve Cryptography over $$ \mathbb{G}\mathbb{F}\left( {2^n } \right) $$ [chapter]

M. Ernst, M. Jung, F. Madlener, S. Huss, R. Blümel
2003 Lecture Notes in Computer Science  
The HW architectures are adapted from Karatsuba's divide and conquer algorithm and allow for a reasonable speedup of the top-level elliptic curve algorithms.  ...  This work describes two generic and scalable architectures of finite field coprocessors, which are implemented within the latest family of Field Programmable System Level Integrated Circuits FPSLIC from  ...  This work was sponsored by and has been done in cooperation with cv cryptovison GmbH, Gelsenkirchen, Germany.  ... 
doi:10.1007/3-540-36400-5_28 fatcat:fjea3dynbvblrn2f3jylhuycd4

Design of elliptic curve cryptoprocessors over GF(2^163) using the Gaussian normal basis

Paulo Cesar Realpe, Vladimir Trujillo-Olaya, Jaime Velasco-Medina
2014 Ingeniería e Investigación  
This paper presents an efficient hardware implementation of cryptoprocessors that perform the scalar multiplication kP over a finite field GF(2 163 ) using two digit-level multipliers.  ...  In this case, the computation times of the multiplication kP using the Lopez-Dahab algorithm, 2-NAF halve-and-add algorithm and 16NAF method for Koblitz curves were 13.37 µs, 16.90 µs and 5.05 µs, respectively  ...  Synthesis results for the cryptoprocessors The synthesis results of the cryptoprocessors over GF(2 163 ) are shown in Table 1 .  ... 
doi:10.15446/ing.investig.v34n2.40542 fatcat:dmv4pxiwgjdkrouy6zmu6j4ihy

Algorithms for Extended Galois Field Generation and Calculation

Zhaneta Savova-Tasheva, Antoniya Tasheva
2015 Mathematical and Software Engineering  
The algorithm analysis shows that the proposed algorithm for finding primitive polynomial is faster than traditional polynomial search and when table operations in GF(pm) are used the algorithms are faster  ...  than traditional polynomial addition and subtraction.  ...  the task of finding a primitive polynomial over GF(p).  ... 
doaj:c0c86476faea490985cc6f9d07a167f1 fatcat:opqa3m7qjrdbdm26py63rrrmae

Implementation of a Hermitian decoder IC in 0.35 /spl mu/m CMOS

J.B. Ashbrook, N.R. Shanbhag, R. Koetter, R.E. Blahut
2001 Proceedings of the IEEE 2001 Custom Integrated Circuits Conference (Cat. No.01CH37169)  
Hermitian codes provide much larger block lengths ( n = 4080) compared to that of the popular Reed-Solomon (RS) codes ( n = 256) over the same field (GF (256) ).  ...  The decoder IC is designed in a 3.3V, 0.35pm, four-metal CMOS process and can correct up to t = 60 errors per block of n = 4080 words at a rate of 400 Mb/s.  ...  RS code synibols over GF(256) can be obtained by eval- uating the data polynomial of degree IC -1 (also defined over GF(256)) over all n = 256 points in GF(256), i.e., points on a line.  ... 
doi:10.1109/cicc.2001.929782 fatcat:5vw7vxt745benmhw5tel77hmfm

Generalized Galois-Fibonacci Matrix Generators Pseudo-Random Sequences

Anatoly Beletsk, National Aviation University, Kyiv, UA, 03058
2021 International Journal of Computer Network and Information Security  
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  ...  The research results are generalized for solving PRNG problems over a Galois field of odd characteristics.  ...  Namely Algorithm for the synthesis of GGM: let n fan irreducible (not necessarily primitive) binary polynomial of degree n and   the primitive element of the field (2 ) n GF , generated by the polynomial  ... 
doi:10.5815/ijcnis.2021.06.05 fatcat:6sw4that7fhzpnnmhiqnudpche

TME Volume 4, Number 2

2007 The Mathematics Enthusiast  
Vol.4, no .2 signals the conclusion of this volume and four years of the journal's existence.  ...  justice, teacher education and the history and philosophy of mathematics and science, in addition to practitioners at all levels.  ...  The relations between flexibility and the shortcuts mentioned in the first part of this paper, and the role of flexibility in the instrumental genesis, apparently, are issues in focus of interest for the  ... 
doi:10.54870/1551-3440.1077 fatcat:yvhyu5dwundsxovkpcwjly3iue

Analysis of efficiency of the bioinspired method for decoding algebraic convolutional codes

Sergii Panchenko, Sergii Prykhodko, Sergii Kozelkov, Mykola Shtompel, Viktor Kosenko, Oleksandr Shefer, Olha Dunaievska
2019 Eastern-European Journal of Enterprise Technologies  
C = =( , , ,...) 0 1 2 with further display of the symbols of field GF q m ( ) into vectors over field GF(q) to obtain the code vector, which corresponds to polynomial (7) : In [10] , it was shown that  ...  non-systematic ( , , ) n k V 0 0 convolutional code with encoding rate R k n = 0 0 over field GF(q), algebraically assigned by generalized generator polynomial (8) or by generator matrix (9) 2.  ... 
doi:10.15587/1729-4061.2019.160753 fatcat:57wu7cu66ff5laepn2b43vrjoi

Page 1160 of Mathematical Reviews Vol. 47, Issue 5 [page]

1974 Mathematical Reviews  
Lempel, Abraham 6659 Analysis and synthesis of polynomials and sequences over GF(2). IEEE Trans. Information Theory IT-17 (1971), 297-303.  ...  Theorem 3: The permutation polynomials X' (t=q"—2), —a?X, and X+a (ae GF(q"), «a#0) form a generating system for the group of reduced permutation polynomials in one variable over GF(q"). A. D.  ... 

Feedback shift registers, 2-adic span, and combiners with memory

Andrew Klapper, Mark Goresky
1997 Journal of Cryptology  
This analysis gives a unified approach to the study of pseudorandom sequences, arithmetic codes, combiners with memory, and the Marsaglia-Zaman random number generator.  ...  Feedback shift registers with carry operation (FCSRs) are described, implemented, and analyzed with respect to memory requirements, initial loading, period, and distributional properties of their output  ...  Acknowledgments We wish to thank Hugh Williams for his help in tracking down the various conjectures and results on primes q with large ord q (2) which are discussed in Section 13.  ... 
doi:10.1007/s001459900024 fatcat:5xza7htdpza5rileekvisnktgy

Linear solutions for cryptographic nonlinear sequence generators

A. Fúster-Sabater, P. Caballero-Gil
2007 Physics Letters A  
Some of these solutions are pseudo-random noise sequences with application in cryptography: the sequences generated by the class of shrinking generators.  ...  This letter shows that linear Cellular Automata based on rules 90/150 generate all the solutions of linear difference equations with binary constant coefficients.  ...  Acknowledgements This work has been supported by Ministerio de Educación y Ciencia (Spain), Projects SEG2004-02418 and SEG2004-04352-C04-03.  ... 
doi:10.1016/j.physleta.2007.04.103 fatcat:blozqfrf4nhovk473sudpfpl5m

VHDL Optimized Model of a Multiplier in Finite Fields

Cecilia Esperanza Sandoval-Ruiz
2017 Ingeniería y Universidad  
Concepts of structural analysis, description of parameterized components, and mathematical treatment of signals have been applied.  ...  This model was described in VHDL, for testing behavior and optimization of hardware.  ...  polynomial of the finite field GF(2 m ).  ... 
doi:10.11144/javeriana.iyu21-2.vhdl fatcat:qtey3nmcljcprkadajtvolba4u

Low-Space Complexity Digit-Serial Multiplier Based on Modified Polynomial Basis Over GF(2m)

Jeng-Shyang Pan, Shu-Xia Dong, Chun-Sheng Yang
2017 Journal of Information Hiding and Multimedia Signal Processing  
According to the properties of Toeplitz matrix, a digit-serial multiplier over GF (2 m ) by irreducible trinomials is presented.  ...  In this paper, in order to reduce the complexities of multiplication, a new polynomial basis is proposed, which is generated by the irreducible trinomial and called modified polynomial basis (MPB).  ...  Next lists generated sequences and complexity analysis for MUX component in the figure 4 .1.  ... 
dblp:journals/jihmsp/0001DY17 fatcat:5hlimclfqvdhvn3p2cq72hci6i
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