Results 1 to 10 of about 600 (30)
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
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
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
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
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
Constructing irreducible polynomials with prescribed level curves over finite fields
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 4, Page 197-200, 2001., 2001 We use Eisenstein′s irreducibility criterion to prove that there exists an absolutely irreducible polynomial P(X, Y) ∈ GF(q)[X, Y] with coefficients in the finite field GF(q) with q elements, with prescribed level curves Xc : = {(x, y) ∈ GF(q)2 | P(x, y) = c}.
Mihai Caragiu
wiley +1 more source
On the decomposition of xd + aexe + ⋯+a1x + a0
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 11, Page 777-781, 2000., 2000 Let K denote a field. A polynomial f(x) ∈ K[x] is said to be decomposable over K if f(x) = g(h(x)) for some polynomials g(x) and h(x) ∈ K[x] with 1 < deg(h) < deg(f). Otherwise f(x) is called indecomposable. If f(x) = g(xm) with m > 1, then f(x) is said to be trivially decomposable.
Javier Gomez-Calderon
wiley +1 more source
The radical factors of f(x) − f(y) over finite fields
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 799-802, 1997., 1996 Let F denote the finite field of order q For f(x) in F[x], let f*(x, y) denote the substitution polynomial f(x) − f(y). The polynomial f*(x, y) has frequently been used in questions on the values set of f(x) In this paper we consider the irreducible factors of f*(x, y) that are “solvable by radicals” We show that if R(x, y) denotes the product of all ...
Javier Gomez-Calderon
wiley +1 more source
Relative rank and regularization
Forum of Mathematics, SigmaWe introduce a new concept of rank – relative rank associated to a filtered collection of polynomials. When the filtration is trivial, our relative rank coincides with Schmidt rank (also called strength).
Amichai Lampert, Tamar Ziegler
doaj +1 more source
Security analysis of ZKPoK based on MQ problem in the multi-instance setting
Journal of Mathematical CryptologyBidoux and Gaborit introduced a new general technique to improve zero-knowledge (ZK) proof-of-knowledge (PoK) schemes for a large set of well-known post-quantum hard computational problems such as the syndrome decoding, the permuted kernel, the rank ...
Kahrobaei Delaram +2 more
doaj +1 more source