Generalizations of Jacobsthal sums and hypergeometric series over finite fields
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DOI: 10.1007/s11139-020-00364-w
Abstract: For non-negative integers $$l_{1}, l_{2},\ldots , l_{n}$$ , we define character sums $$\varphi _{(l_{1}, l_{2},\ldots , l_{n})}$$ and $$\psi _{(l_{1}, l_{2},\ldots , l_{n})}$$ over a finite field which are generalizations of Jacobsthal and modified Jacobsthal… read more here.
Keywords: generalizations jacobsthal; hypergeometric series; finite field; series ... See more keywords
On Diophantine exponents for Laurent series over a finite field
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DOI: 10.1016/j.jnt.2017.09.008
Abstract: Abstract In this paper, we study the properties of Diophantine exponents w n and w n ⁎ for Laurent series over a finite field. We prove that for an integer n ≥ 1 and a… read more here.
Keywords: exponents laurent; finite field; diophantine exponents; laurent series ... See more keywords
Density of Periodic Points for Lattès maps over Finite Field
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DOI: 10.1016/j.jnt.2021.10.009
Abstract: Let Ld be the Lattès map associated to the multiplication-by-d endomorphism of an elliptic curve E defined over a finite field Fq. We determine the density δ(Ld, q) of periodic points for Ld in P(Fq).… read more here.
Keywords: periodic points; points latt; density periodic; finite field ... See more keywords
Transcendence degree one function fields over a finite field with many automorphisms
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Pure and Applied Algebra"
DOI: 10.1016/j.jpaa.2017.08.008
Abstract: Abstract Let K be the algebraic closure of a finite field F q of odd characteristic p . For a positive integer m prime to p , let F = K ( x , y… read more here.
Keywords: finite field; many automorphisms; transcendence degree; field ... See more keywords
On the Finite Field Cone Restriction Conjecture in Four Dimensions and Applications in Incidence Geometry
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DOI: 10.1093/imrn/rnab201
Abstract: The first purpose of this paper is to solve completely the finite field cone restriction conjecture in four dimensions with $-1$ non-square. The second is to introduce a new approach to study incidence problems via… read more here.
Keywords: restriction; restriction conjecture; finite field; field cone ... See more keywords
Area-Efficient Finite Field Multiplication Using Hybrid SET-MOS Technology
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Circuits and Systems I: Regular Papers"
DOI: 10.1109/tcsi.2022.3186810
Abstract: Single-electron transistors (SETs) exhibit a unique characteristic of Coulomb oscillation which can find many digital applications with area efficiency. More specifically, both MOS and SET devices can be used to implement XOR gates with almost… read more here.
Keywords: set mos; area; finite field; hybrid set ... See more keywords
Cluster Synchronization of Finite-Field Networks.
Sign Up to like & getrecommendations! Published in 2023 at "IEEE transactions on cybernetics"
DOI: 10.1109/tcyb.2023.3273571
Abstract: This technical paper investigates the cluster synchronization of finite-field networks (FFNs) based on the algebraic state space representation. By resorting to the semi-tensor product of matrices, the cluster synchronization of an FFN can be completely… read more here.
Keywords: field networks; synchronization finite; finite field; cluster synchronization ... See more keywords
Synchronization of Finite-Field Networks With Time Delays
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Network Science and Engineering"
DOI: 10.1109/tnse.2021.3115891
Abstract: In this paper, finite-field networks (FFNs) with time delays are investigated. We analyze the dynamics of FFNs with time delays in view of linear recursion theory. It is shown that delayed FFNs behave in a… read more here.
Keywords: time; field networks; finite field; delayed ffns ... See more keywords
An Efficient and High-Speed Overlap-Free Karatsuba-Based Finite-Field Multiplier for FGPA Implementation
Sign Up to like & getrecommendations! Published in 2021 at "IEEE Transactions on Very Large Scale Integration (VLSI) Systems"
DOI: 10.1109/tvlsi.2021.3058509
Abstract: Cryptography systems have become inseparable parts of almost every communication device. Among cryptography algorithms, public-key cryptography, and in particular elliptic curve cryptography (ECC), has become the most dominant protocol at this time. In ECC systems,… read more here.
Keywords: implementation; field; speed overlap; high speed ... See more keywords
An Optimized M-Term Karatsuba-Like Binary Polynomial Multiplier for Finite Field Arithmetic
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DOI: 10.1109/tvlsi.2022.3148207
Abstract: Finite field multiplication is a fundamental and frequently used operation in various cryptographic circuits and systems. Because of its high complexity, this operation generally determines the overall complexity and cost of these systems. Therefore, finite… read more here.
Keywords: term karatsuba; optimized term; finite field; karatsuba like ... See more keywords
Reliable Architectures for Finite Field Multipliers Using Cyclic Codes on FPGA Utilized in Classic and Post-Quantum Cryptography
Sign Up to like & getrecommendations! Published in 2023 at "IEEE Transactions on Very Large Scale Integration (VLSI) Systems"
DOI: 10.1109/tvlsi.2022.3224357
Abstract: Fault detection is becoming greatly important in protecting cryptographic designs that can suffer from both natural or malicious faults. Finite fields over $\text {GF}(2^{m})$ are widely used in such designs, since their data are coded… read more here.
Keywords: multipliers using; post quantum; finite field; field multipliers ... See more keywords