Results 11 to 20 of about 176,423 (294)
IACR Transactions on Symmetric Cryptology, 2022 There are many recent results on reverse-engineering (potentially hidden) structure in cryptographic S-boxes. The problem of recovering structure in the other main building block of symmetric cryptographic primitives, namely, the linear layer, has not ...
Christof Beierle +3 more
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On the multiplicative order of elements in Wiedemann's towers of finite fields
Karpatsʹkì Matematičnì Publìkacìï, 2015 We consider recursive binary finite field extensions $E_{i+1} =E_{i} (x_{i+1} )$, $i\ge -1$, defined by D. Wiedemann. The main object of the paper is to give some proper divisors of the Fermat numbers $N_{i} $ that are not equal to the multiplicative ...
R. Popovych
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Information, 2021 Linear complexity is an important criterion to characterize the unpredictability of pseudo-random sequences, and large linear complexity corresponds to high cryptographic strength.
Jiang Ma +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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On the number of solutions of two-variable diagonal quartic equations over finite fields
AIMS Mathematics, 2020 Let $p$ be a odd prime number and let $\mathbb{F}_q$ be the finite field of characteristic $p$ with $q$ elements. In this paper, by using the Gauss sum and Jacobi sum, we give an explicit formula for the number $N(x_1^4+x_2^4=c)$ of solutions of the ...
Junyong Zhao, Yang Zhao, Yujun Niu
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Classification of Elements in Elliptic Curve Over the Ring 𝔽q[ɛ]
Discussiones Mathematicae - General Algebra and Applications, 2021 Let 𝔽q[ɛ] := 𝔽q [X]/(X4 − X3) be a finite quotient ring where ɛ4 = ɛ3, with 𝔽q is a finite field of order q such that q is a power of a prime number p greater than or equal to 5.
Selikh Bilel +2 more
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Elements of high order in finite fields specified by binomials
Karpatsʹkì Matematičnì Publìkacìï, 2022 Let $F_q$ be a field with $q$ elements, where $q$ is a power of a prime number $p\geq 5$. For any integer $m\geq 2$ and $a\in F_q^*$ such that the polynomial $x^m-a$ is irreducible in $F_q[x]$, we combine two different methods to explicitly construct ...
V. Bovdi, A. Diene, R. Popovych
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On multiplication in finite fields
Journal of Complexity, 2010 AbstractWe present a method for multiplication in finite fields which gives multiplication algorithms with improved or best known bilinear complexities for certain finite fields. Our method generalizes some earlier methods and combines them with the recently introduced complexity notion M̂q(ℓ), which denotes the minimum number of multiplications needed
Cenk, Murat, Ozbudak, Ferruh
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Elliptic periods for finite fields [PDF]
Finite Fields and Their Applications, 2009 We construct two new families of basis for finite field extensions. Basis in the first family, the so-called elliptic basis, are not quite normal basis, but they allow very fast Frobenius exponentiation while preserving sparse multiplication formulas. Basis in the second family, the so-called normal elliptic basis are normal basis and allow fast (quasi
Couveignes, Jean-Marc, Lercier, Reynald
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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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