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

2007
*
Proceedings of the ... IEEE VLSI Test Symposium
*

In this article, a C-testable design for detecting transition faults in the

doi:10.1109/vts.2007.83
dblp:conf/vts/RahamanMSP07
fatcat:yrpiygeflvhorgcniejegctavq
*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*) . ...##
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$\textrm{GF}(2^m)$ Finite-Field Multipliers with Reduced Activity Variations
[chapter]

2012
*
Lecture Notes in Computer Science
*

In this work, we present

doi:10.1007/978-3-642-31662-3_11
fatcat:bxdr7zzfgfafliluucqwn7qiee
*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 }. ...##
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Modelling nonlinear sequence generators in terms of linear cellular automata

2007
*
Applied Mathematical Modelling
*

The linearity

doi:10.1016/j.apm.2005.08.013
fatcat:u6hwyco5frfvrhjgeh2vvrvpa4
*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*...##
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A Reconfigurable System on Chip Implementation for Elliptic Curve Cryptography over $$ \mathbb{G}\mathbb{F}\left( {2^n } \right) $$
[chapter]

2003
*
Lecture Notes in Computer Science
*

The HW architectures are adapted from Karatsuba's divide

doi:10.1007/3-540-36400-5_28
fatcat:fjea3dynbvblrn2f3jylhuycd4
*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. ...##
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Design of elliptic curve cryptoprocessors over GF(2^163) using the Gaussian normal basis

2014
*
Ingeniería e Investigación
*

This paper presents an efficient hardware implementation

doi:10.15446/ing.investig.v34n2.40542
fatcat:dmv4pxiwgjdkrouy6zmu6j4ihy
*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*16NAF 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 . ...##
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Algorithms for Extended Galois Field Generation and Calculation

2015
*
Mathematical and Software Engineering
*

The algorithm

doaj:c0c86476faea490985cc6f9d07a167f1
fatcat:opqa3m7qjrdbdm26py63rrrmae
*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). ...##
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Implementation of a Hermitian decoder IC in 0.35 /spl mu/m CMOS

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

doi:10.1109/cicc.2001.929782
fatcat:5vw7vxt745benmhw5tel77hmfm
*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. ...##
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Generalized Galois-Fibonacci Matrix Generators Pseudo-Random Sequences

2021
*
International Journal of Computer Network and Information Security
*

This effect is achieved both due to the rise in the number

doi:10.5815/ijcnis.2021.06.05
fatcat:6sw4that7fhzpnnmhiqnudpche
*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*...##
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TME Volume 4, Number 2

2007
*
The Mathematics Enthusiast
*

Vol.4, no .

doi:10.54870/1551-3440.1077
fatcat:yvhyu5dwundsxovkpcwjly3iue
*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 ...##
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Analysis of efficiency of the bioinspired method for decoding algebraic convolutional codes

2019
*
Eastern-European Journal of Enterprise Technologies
*

C = =( , , ,...) 0 1

doi:10.15587/1729-4061.2019.160753
fatcat:57wu7cu66ff5laepn2b43vrjoi
*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*. ...##
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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. ...##
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Feedback shift registers, 2-adic span, and combiners with memory

1997
*
Journal of Cryptology
*

This

doi:10.1007/s001459900024
fatcat:5xza7htdpza5rileekvisnktgy
*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. ...##
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Linear solutions for cryptographic nonlinear sequence generators

2007
*
Physics Letters A
*

Some

doi:10.1016/j.physleta.2007.04.103
fatcat:blozqfrf4nhovk473sudpfpl5m
*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. ...##
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VHDL Optimized Model of a Multiplier in Finite Fields

2017
*
Ingeniería y Universidad
*

Concepts

doi:10.11144/javeriana.iyu21-2.vhdl
fatcat:qtey3nmcljcprkadajtvolba4u
*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 ). ...##
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Low-Space Complexity Digit-Serial Multiplier Based on Modified Polynomial Basis Over GF(2m)

2017
*
Journal of Information Hiding and Multimedia Signal Processing
*

According to the properties

dblp:journals/jihmsp/0001DY17
fatcat:5hlimclfqvdhvn3p2cq72hci6i
*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. ...
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