Journal ArticleDOI
A VLSI design for computing exponentiations in GF(2/sup m/) and its application to generate pseudorandom number sequences
C.C. Wang,D. Pei +1 more
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An algorithm to generate a relatively long pseudorandom number sequence is presented and it is shown that the period of this sequence is significantly increased compared to that of the sequence generated by the most commonly used maximal length shift register scheme.Abstract:
A VLSI design for computing exponentiation in finite fields is developed. An algorithm to generate a relatively long pseudorandom number sequence is presented. It is shown that the period of this sequence is significantly increased compared to that of the sequence generated by the most commonly used maximal length shift register scheme. >read more
Citations
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Journal ArticleDOI
Efficient semisystolic architectures for finite-field arithmetic
TL;DR: This paper explores and classify algorithms for finite field multiplication, squaring, and exponentiation into least significant bit first (LSB-first) scheme and most significantbit first (MSB- first) scheme, and implements these algorithms using semisystolic arrays.
Journal ArticleDOI
Optimal normal bases
Shuhong Gao,Hendrik W. Lenstra +1 more
TL;DR: The present paper determines all optimal normal bases for a finite Galois extension of fields, of degree n, and confirms a conjecture that was made by Mullin et al. on the basis of a computer search.
Normal Bases over Finite Fields
TL;DR: The principal result in the thesis is the complete determination of all optimal normal bases in finite fields, which confirms a conjecture by Mullin, Onyszchuk, Vanstone and Wilson.
Journal ArticleDOI
Fast arithmetic for public-key algorithms in Galois fields with composite exponents
TL;DR: A novel class of arithmetic architectures for Galois fields GF(2/sup k/) is described, capable of exploring the time-space trade-off paradigm in a flexible manner and two different approaches to squaring are provided.
Journal ArticleDOI
Efficient multiplier architectures for Galois fields GF(2/sup 4n/)
C. Paar,P. Fleischmann,P. Roeise +2 more
TL;DR: A new class of multipliers for finite fields GF((2/sup n/)/sup 4/) is introduced, based on a modified version of the Karatsuba-Ofman algorithm, which leads to architectures which show a considerably improved gate complexity compared to traditional approaches and reduced delay if compared with KOA-based architectures with separate module reduction.
References
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Book
The Theory of Error-Correcting Codes
TL;DR: This book presents an introduction to BCH Codes and Finite Fields, and methods for Combining Codes, and discusses self-dual Codes and Invariant Theory, as well as nonlinear Codes, Hadamard Matrices, Designs and the Golay Code.
Journal ArticleDOI
VLSI Architectures for Computing Multiplications and Inverses in GF(2 m )
TL;DR: In this article, a pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m) with the simple squaring property of the normal basis representation used together with this multiplier.
Patent
Computational method and apparatus for finite field arithmetic
Jimii Kei Oomura,James L. Massey +1 more
TL;DR: In this article, the GF(2 m ) elements are represented by a vector of m binary digits in such a way that multiplication can be performed by using the same logic function to compute each binary component of the product of two elements, and addition can be formed by logic circuitry that forms the modulo-two sum of the corresponding components of the two vectors representing the elements to be summed.