Results 21 to 30 of about 1,050,138 (224)
Arithmetic in a finite field [PDF]
Mathematics of Computation, 1980 An algorithm for realizing finite field arithmetic is presented. The relationship between linear recursions and polynomial arithmetic (modulo a fixed polynomial) over Zp is exploited to reduce the storage and computation requirements of the algorithm. A primitive normal polynomial is used to simplify the calculation of multiplicative inverses.
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Strict avalanche criterion over finite fields
Journal of Mathematical Cryptology, 2007 Boolean functions which satisfy the Strict Avalanche Criterion (SAC) play an important role in the art of information security. In this paper, we extend the concept of SAC to finite fields GF(p).
Li Yuan, Cusick T. W.
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Computation with finite fields
Information and Control, 1963 A technique for systematically generating representations of finite fields is presented. Relations which must be physically realized in order to implement a parallel arithmetic unit to add, multiply, and divide elements of finite fields of 2n elements are obtained.
Thomas C. Bartee, David I. Schneider
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Finite H_v-Fields with Strong-Inverses
Ratio Mathematica, 2017 The largest class of hyperstructures is the class of H v -structures. This is the class of hyperstructures where the equality is replaced by the non-empty intersection.
Theodora Kaplani, Thomas Vougiouklis
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Proceedings of the American Mathematical Society, 1962 Let \(F^*\) be the multiplicative group of non-zero elements of \(\mathrm{GF}(p^n)\) where \(p\) is a prime; set \(p^n-1 = rs\) where \((r, s) = 1\), \(r < s\) and \(r\not\equiv 1 \bmod p\). \(F^*\) has subgroups \(Y, Z\) of orders \(r, s\) respectively and every element \(\xi\) of \(F^*\) can be expressed uniquely in the form \(\xi = \eta\zeta\) with \
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The Hartley transform in a finite field [PDF]
ITS'98 Proceedings. SBT/IEEE International Telecommunications Symposium (Cat. No.98EX202), 1999 7 pages, IEEE/SBT International Telecommunication Symposium, ITS, 1998, Sao Paulo ...
Ricardo M. Campello de Souza +2 more
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On permutation polynomials over finite fields
International Journal of Mathematics and Mathematical Sciences, 1987 A polynomial f over a finite field F is called a permutation polynomial if the mapping F→F defined by f is one-to-one. In this paper we consider the problem of characterizing permutation polynomials; that is, we seek conditions on the coefficients of a ...
R. A. Mollin, C. Small
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Parallel machine arithmetic for recurrent number systems in non-quadratic fields [PDF]
Компьютерная оптика, 2020 The paper proposes a new method of synthesis of computer arithmetic systems for "error-free" parallel calculations. The difference between the proposed approach and calculations in traditional systems of Residue Number Systems for the direct sum of ...
Vladimir Chernov
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A Generalization of APN Functions for Odd Characteristic [PDF]
, 2016 Almost perfect nonlinear (APN) functions on finite fields of characteristic two have been studied by many researchers. Such functions have useful properties and applications in cryptography, finite geometries and so on.
Kuroda, Masamichi, Tsujie, Shuhei
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Lamps, Factorizations and Finite Fields
, 1999 I answer a question from the 1993 International Mathematical Olympiads by constructing an equivalent algebraic problem, and unearth a surprising behaviour of some polynomials over the two-element field.Comment: 6 pages, elementary ...
Bartholdi, Laurent
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