Results 21 to 30 of about 635 (41)

Relative rank and regularization

Forum of Mathematics, Sigma
We 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

Squares and difference sets in finite fields [PDF]

, 2013
For infinitely many primes p = 4k+1 we give a slightly improved upper bound for the maximal cardinality of a set B ⊂ Z p such that the difference set B−B contains only quadratic residues. Namely, instead of the ”trivial” bound |B| ≤ √p we prove |B √p
Bachoc, C., Matolcsi, Máté, Ruzsa, Z. Imre   +2 more
core  

Counting irreducible binomials over finite fields

, 2015
We consider various counting questions for irreducible binomials over finite fields.
Heyman, Randell, Shparlinski, Igor E.
core   +1 more source

A result on polynomials derived via graph theory

, 2019
We present an example of a result in graph theory that is used to obtain a result in another branch of mathematics. More precisely, we show that the isomorphism of certain directed graphs implies that some trinomials over finite fields have the same ...
Coulter, Robert S., De Winter, Stefaan, Kodess, Alex, Lazebnik, Felix   +3 more
core   +1 more source

Non-unique factorization of polynomials over residue class rings of the integers

, 2011
We investigate non-unique factorization of polynomials in Z_{p^n}[x] into irreducibles. As a Noetherian ring whose zero-divisors are contained in the Jacobson radical, Z_{p^n}[x] is atomic.
Anderson D. D., Christopher Frei, Frisch S., McDonald B. R., Sophie Frisch, Wan Z.-X.   +5 more
core   +1 more source

Security analysis of ZKPoK based on MQ problem in the multi-instance setting

Journal of Mathematical Cryptology
Bidoux 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, Perret Ludovic, Vigorito Martina   +2 more
doaj   +1 more source

A Swan-like note for a family of binary pentanomials

, 2018
In this note, we employ the techniques of Swan (Pacific J. Math. 12(3): 1099-1106, 1962) with the purpose of studying the parity of the number of the irreducible factors of the penatomial $X^n+X^{3s}+X^{2s}+X^{s}+1\in\mathbb{F}_2[X]$, where $s$ is even ...
Kapetanakis, Giorgos
core   +1 more source

Inner product functional encryption based on the UOV scheme

Journal of Mathematical Cryptology
We analyze the efficiency and security of the inner product functional encryption (IPFE) protocol introduced in 2021 by Debnath, Mesnager, Dey, and Kundu, specifically when instantiated with UOV.
La Scala Roberto, Meneghetti Alessio
doaj   +1 more source

Value sets of bivariate Chebyshev maps over finite fields

, 2015
We determine the cardinality of the value sets of bivariate Chebyshev maps over finite fields. We achieve this using the dynamical properties of these maps and the algebraic expressions of their fixed points in terms of roots of unity.Comment: 11 pages ...
Küçüksakallı, Ömer
core   +1 more source

Fuchs' problem for indecomposable abelian groups

, 2015
More than 50 years ago, Laszlo Fuchs asked which abelian groups can be the group of units of a commutative ring. Though progress has been made, the question remains open.
Chebolu, Sunil K., Lockridge, Keir
core   +1 more source