Results 61 to 70 of about 879 (182)

The unit group of algebra of circulant matrices [PDF]

International Journal of Group Theory, 2014
Let $Cr_{n}(F)$ denote the algebra of $n times n$ circulant matrices over the field $F$. In this paper, we study the unit group of $Cr_{n}(F_{p^m})$, where $F_{p^m}$ denotes the Galois field of order $p^{m}$, $p$ prime.
Neha Makhijani , 2R. K. Sharma, J. B. Srivastava   +2 more
doaj  

Galois Field Instructions in the Sandblaster 2.0 Architectrue

International Journal of Digital Multimedia Broadcasting, 2009
This paper presents a novel approach to implementing multiplication of Galois Fields with 2N. Elements of GF(2N) can be represented as polynomials of degree less than N over GF(2).
Mayan Moudgill, Andrei Iancu, Daniel Iancu   +2 more
doaj   +1 more source

Format-preserving encryption algorithm based on dynamic galois field

Dianxin kexue
Format-preserving encryption (FPE) is characterized by its ability to maintain data format and length post-encryption while adhering to format constraints, rendering it highly applicable for data anonymization purposes. Current FPE schemes are faced with
YUAN Heqing, SHEN Jinshang, WANG Qiang
doaj  

A Novel Image Encryption Technique Based on Cyclic Codes over Galois Field. [PDF]

Comput Intell Neurosci, 2022
Asif M, Asamoah JKK, Hazzazi MM, Alharbi AR, Ashraf MU, Alghamdi AM, Alghamdi AM.   +6 more
europepmc   +1 more source

CONSTRUCTION OF SUBSTITUTION BOX (S-BOX) BASED ON IRREDUCIBLE POLYNOMIALS ON GF(2^8)

Barekeng
In the field of modern encryption algorithms, the creation of S-Box is an essential element that plays an important role in maintaining data security in various industries.
Faldy Tita, Adi Setiawan, Bambang Susanto   +2 more
doaj   +1 more source

Computing character degrees via a Galois connection [PDF]

International Journal of Group Theory, 2015
In a previous paper, the second author established that, given finite fields ...
Mark L. Lewis , John K. McVey
doaj  

Practice of the Incomplete $p$-Ramification Over a Number Field -- History of Abelian $p$-Ramification

Communications in Advanced Mathematical Sciences, 2019
The theory of $p$-ramification, regarding the Galois group of the maximal pro-$p$-extension of a number field $K$, unramified outside $p$ and $\infty$, is well known including numerical experiments with PARI/GP programs.
Georges Gras
doaj   +1 more source

Algorithm for Obtaining Complete Irreducible Polynomials over Given Galois Field for New Method of Digital Monitoring of Information Space

Computers
Irreducible polynomials are widely used in modern cryptography; however, algorithms for finding such polynomials remain quite complex and require significant computational resources.
Dina Shaltykova, Aliya Massalimova, Yelizaveta Vitulyova, Ibragim Suleimenov   +3 more
doaj   +1 more source

Quadratic subfields on quartic extensions of local fields

International Journal of Mathematics and Mathematical Sciences, 1988
We show that any quartic extension of a local field of odd residue characteristic must contain an intermediate field. A consequence of this is that local fields of odd residue characteristic do not have extensions with Galois group A4 or S4 ...
Joe Repka
doaj   +1 more source

DIFFERENTIATION OF POLYNOMIALS IN SEVERAL VARIABLES OVER GALOIS FIELDS OF FUZZY CARDINALITY AND APPLICATIONS TO REED-MULLER CODES

Advanced Engineering Research, 2018
Introduction. Polynomials in several variables over Galois fields provide the basis for the Reed-Muller coding theory, and are also used  in a number of cryptographic problems.
V. M. Deundyak, N. S. Mogilevskaya
doaj   +1 more source