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pro vyhledávání: '"Binary fields"'
Autor:
Sall, Mohamadou, Hasan, M. Anwar
Binary field extensions are fundamental to many applications, such as multivariate public key cryptography, code-based cryptography, and error-correcting codes. Their implementation requires a foundation in number theory and algebraic geometry and ne
Externí odkaz:
http://arxiv.org/abs/2402.11544
Autor:
Ahmadi, Omran, Shafaeiabr, Masoud
We confirm a conjecture of Cun Sheng Ding~\cite{Ding-Discrete} claiming that the punctured value-sets of a list of eleven trinomials over odd-degree extensions of the binary field give rise to difference sets with Singer parameters. In the course of
Externí odkaz:
http://arxiv.org/abs/2108.10042
Akademický článek
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In this paper, new results on convolution of spectral components in binary fields have been presented for combiatorial sequences. A novel method of convolution of DFT points through Chinese Remainder Theorem (CRT) is presented which has lower complex
Externí odkaz:
http://arxiv.org/abs/1911.11437
Autor:
Chilikov, Alexey
The description of the image of cubic function $f(x) = x^3+x$ over finite field $F_{2^n}$ was stated as a problem in the NSUCrypto olympiad in 2017. This problem was marked by organizers as <>. In this work we propose the full solution of t
Externí odkaz:
http://arxiv.org/abs/1912.06486
We introduce a new class of irreducible pentanomials over $\mathbb{F}_2$ of the form $f(x) = x^{2b+c} + x^{b+c} + x^b + x^c + 1$. Let $m=2b+c$ and use $f$ to define the finite field extension of degree $m$. We give the exact number of operations requ
Externí odkaz:
http://arxiv.org/abs/1806.00432
Publikováno v:
Applied Sciences, Vol 13, Iss 19, p 10882 (2023)
This article proposes a flexible hardware accelerator optimized from a throughput and area point of view for the computationally intensive part of elliptic curve cryptography. The target binary fields, defined by the National Institute of Standards a
Externí odkaz:
https://doaj.org/article/481e450eb9b949aba7e90c0d50e2d6d4
For binary $[n,k,d]$ linear locally repairable codes (LRCs), two new upper bounds on $k$ are derived. The first one applies to LRCs with disjoint local repair groups, for general values of $n,d$ and locality $r$, containing some previously known boun
Externí odkaz:
http://arxiv.org/abs/1701.05989
Autor:
Lanzone, Valentino, Nagy, Gábor P.
Publikováno v:
Acta Sci. Math. (Szeged) 80:3-4(2014), 409-418
The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing computations over
Externí odkaz:
http://arxiv.org/abs/1501.03662
Akademický článek
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