Results 21 to 30 of about 176,578 (264)
Formalized MathematicsSummary We continue the formalization of field theory in Mizar. Here we prove existence and uniqueness of finite fields by constructing the splitting field of the polynomial X (p n
Louis Halle Rowen, Uzi Vishne
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Constructions of pseudorandom binary lattices using cyclotomic classes in finite fields
Open Mathematics, 2020 In 2006, Hubert, Mauduit and Sárközy extended the notion of binary sequences to n-dimensional binary lattices and introduced the measures of pseudorandomness of binary lattices.
Chen Xiaolin
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On multiplication in finite fields
Journal of Complexity, 2010 The authors introduce complexity notions and give a brief review of algebraic fields. They propose a method for multiplication in finite fields. The method is shown to be a significant improvement over the best known bilinear complexities for certain finite fields.
Murat Cenk, Ferruh Özbudak
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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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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.
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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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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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FINITE UNDECIDABILITY IN NIP FIELDS
The Journal of Symbolic Logic, 2023 AbstractA field K in a ring language $\mathcal {L}$ is finitely undecidable if $\mbox {Cons}(T)$ is undecidable for every nonempty finite $T \subseteq {\mathtt{Th}}(K; \mathcal {L})$ . We extend a construction of Ziegler and (among other results) use a first-order classification of Anscombe and Jahnke to prove every NIP henselian nontrivially ...
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Lookup Table-Based Design of Scalar Multiplication for Elliptic Curve Cryptography
CryptographyThis paper is aimed at using a lookup table method to improve the scalar multiplication performance of elliptic curve cryptography. The lookup table must be divided into two polynomials and requires two iterations of point doubling operation, for which ...
Yan-Duan Ning +3 more
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Lower Bound of the Complexity of Seven-Valued Functions in the Class of Polarized Polynomials
Известия Иркутского государственного университета: Серия "Математика", 2017 One of the directions of the investigation of functions over finite fields is the study of their representations, including polynomial ones. In the area of polynomial representations of functions the problem of estimating the complexity of such ...
A.S. Baliuk, A.S. Zinchenko
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