Results 31 to 40 of about 12,115,560 (297)

A Robust Version of Heged\H{u}s's Lemma, with Applications [PDF]

TheoretiCS, 2023
Heged\H{u}s's lemma is the following combinatorial statement regarding polynomials over finite fields. Over a field $\mathbb{F}$ of characteristic $p > 0$ and for $q$ a power of $p$, the lemma says that any multilinear polynomial $P\in \mathbb{F}[x_1 ...
Srikanth Srinivasan
doaj   +1 more source

Reversed Dickson polynomials over finite fields [PDF]

, 2009
Reversed Dickson polynomials over finite fields are obtained from Dickson polynomials Dn(x,a) over finite fields by reversing the roles of the indeterminate x and the parameter a. We study reversed Dickson polynomials with emphasis on their permutational
Hou, Xiang-dong, Mullen, Gary L., Yucas, Joseph L., Sellers, James A.   +3 more
core   +1 more source

Polynomials over Finite Fields

, 2020
U ovom radu bavili smo se polinomima i njihovim svojstvima, a posebno svojstvima polinoma nad konačnim poljima. U prvom poglavlju dane su osnovne definicije i tvrdnje vezane uz djeljivost polinoma, faktorizaciju, korijene i ireducibilnost polinoma ...
Bročić, Lucija
core   +2 more sources

Factoring with Pell conics

Lietuvos Matematikos Rinkinys, 2004
In the paper the Pell conics method for factoring integers, based on observations of Lemmer­meyer [2, 3], is presented explicitly. Moreover, a similar algorithm for factoring polynomials over finite fields is given.
Rasa Šleževičienė
doaj   +3 more sources

Etale and crystalline companions, I [PDF]

Épijournal de Géométrie Algébrique, 2022
Let $X$ be a smooth scheme over a finite field of characteristic $p$. Consider the coefficient objects of locally constant rank on $X$ in $\ell$-adic Weil cohomology: these are lisse Weil sheaves in \'etale cohomology when $\ell \neq p$, and ...
Kiran S. Kedlaya
doaj   +1 more source

Irreducible compositions of polynomials over finite fields [PDF]

Designs, Codes and Cryptography, 2010
The paper studies constructions of irreducible polynomials over finite fields using polynomial composition method.
Melsik K. Kyuregyan, Gohar M. Kyureghyan
openaire   +2 more sources

Sequences over Finite Fields Defined by OGS and BN-Pair Decompositions of PSL₂(q) Connected to Dickson and Chebyshev Polynomials

Mathematics, 2023
The factorization of groups into a Zappa–Szép product, or more generally into a k-fold Zappa–Szép product of its subgroups, is an interesting problem, since it eases the multiplication of two elements in a group and has recently been applied to public ...
Robert Shwartz, Hadas Yadayi
doaj   +1 more source

Multiplication polynomials and relative Manin-Mumford [PDF]

, 2015
After the introduction we prove in chapter 2 that the resultant of the standard multiplication polynomials $A_n,B_n$ of an elliptic curve in the form $y^2 = x^3+ax+b$ is
$(16\Delta)^{{n^2(n^2-1) \over 6}}$, where $\Delta=-(4a^3+27b^2)$ is the ...
Schmidt, Harry
core   +1 more source

On the Structure of Valiant's Complexity Classes [PDF]

Discrete Mathematics & Theoretical Computer Science, 1999
In Valiant developed an algebraic analogue of the theory of NP-completeness for computations of polynomials over a field. We further develop this theory in the spirit of structural complexity and obtain analogues of well-known results by Baker, Gill, and
Peter Bürgisser
doaj   +3 more sources

Classes of weak Dembowski–Ostrom polynomials for multivariate quadratic cryptosystems

Journal of Mathematical Cryptology, 2015
T. Harayama and D. K. Friesen [J. Math. Cryptol. 1 (2007), 79–104] proposed the linearized binomial attack for multivariate quadratic cryptosystems and introduced weak Dembowski–Ostrom (DO) polynomials in this framework over the finite field 𝔽2.
Alam Bilal, Özbudak Ferruh, Yayla Oğuz
doaj   +1 more source