Results 1 to 10 of about 71 (43)
On the Nonexistence of Partial Difference Sets by Projections to Finite Fields
Communications in Mathematical Research, 2022 In the study of (partial) difference sets and their generalizations in groups G, the most widely used method is to translate their definition into an equation over group ring Z[G] and to investigate this equation by applying complex representations of G.
Yue Zhou
semanticscholar +1 more source
The Oribatida v1.3 Family of Lightweight Authenticated Encryption Schemes
Journal of Mathematical Cryptology, 2021 Permutation-based modes have been established for lightweight authenticated encryption, as can be seen from the high interest in the ongoing NIST lightweight competition.
Bhattacharjee Arghya +3 more
doaj +1 more source
On computing factors of cyclotomic polynomials [PDF]
arXiv.org, 1993 For odd square-free n > 1 the cyclotomic polynomial Φn(x) satisfies the identity of Gauss 4Φn(x) = An − (−1)(n−1)/2nB2 n. A similar identity of Aurifeuille, Le Lasseur and Lucas is Φn((−1)x) = C n − nxD n or, in the case that n is even and square-free ...
Richard P. Brent
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The strong primitive normal basis theorem [PDF]
, 2006 An element α of the extension E of degree n over the finite field F = GF(q) is called free over F if {α, α q , . . . , α q n 1 } is a (normal) basis of E/F.
S. Cohen, Sophie Huczynska
semanticscholar +1 more source
Efficiently Processing Complex-Valued Data in Homomorphic Encryption
Journal of Mathematical Cryptology, 2020 We introduce a new homomorphic encryption scheme that is natively capable of computing with complex numbers. This is done by generalizing recent work of Chen, Laine, Player and Xia, who modified the Fan–Vercauteren scheme by replacing the integral ...
Bootland Carl +3 more
doaj +1 more source
Quasi-subfield Polynomials and the Elliptic Curve Discrete Logarithm Problem
Journal of Mathematical Cryptology, 2020 We initiate the study of a new class of polynomials which we call quasi-subfield polynomials. First, we show that this class of polynomials could lead to more efficient attacks for the elliptic curve discrete logarithm problem via the index calculus ...
Huang Ming-Deh +4 more
doaj +1 more source
Can we Beat the Square Root Bound for ECDLP over 𝔽p2 via Representation?
Journal of Mathematical Cryptology, 2020 We give a 4-list algorithm for solving the Elliptic Curve Discrete Logarithm (ECDLP) over some quadratic field 𝔽p2. Using the representation technique, we reduce ECDLP to a multivariate polynomial zero testing problem.
Delaplace Claire, May Alexander
doaj +1 more source
Carlitz-Wan conjecture for permutation polynomials and Weill bound for curves over finite fields
Finite Fields Their Appl., 2018 Article history: Received 27 September 2013 Received in revised form 1 June 2018 Accepted 5 June 2018 Available online 23 August 2018 Communicated by Rudolf Lidl MSC: 11T06 11G20 ...
J. Chahal, S. Ghorpade
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On the roots of the substitution Dickson polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 6, Page 349-353, 2002., 2002 We show that under the composition of multivalued functions, the set of the y‐radical roots of the Dickson substitution polynomial gd(x, a) − gd(y, a) is generated by one of the roots. Hence, we show an expected generalization of the fact that, under the composition of the functions, the y‐radical roots of xd − yd are generated by ζdy.
Javier Gomez-Calderon
wiley +1 more source