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58.775  Articles
1 of 5.879 pages  |  10  records  |  more records»
Context. The problem to form generalized primitive matrixes on the Galois and Fibonacci any order over the field characteristics2 for the construction by the generators gamma functions for cryptographically stable algorithms of inline data encryption, fre... see more

Context. The problem to form generalized primitive matrixes on the Galois and Fibonacci any order over the field characteristics2 for the construction by the generators gamma functions for cryptographically stable algorithms of inline data encryption, fre... see more

Context. When cryptographic applications and data transmission control systems are implementing, there is a need for quick methods for performing operations on finite field elements. The object of the study is the processes of encryption, decryption and t... see more

This paper presents how the steps that used to determine a multiplicative inverse by method based on the Euclidean algorithm, can be used to find a greatest common divisor for polynomials in the Galois field (2^n ).

The questions of Galois and Fibonacci random size n primitive matrices creation over thesimple field GF( p) is considered. The synthesis is based on usage of irreducible polynomial fn of degreen and primitive elements of extended field GF( pn ) , which is... see more

A  series  of  experiments  has  been  conducted  to  show  that  FPGA synthesis  of  Galois-Field  (GF)  based  arithmetic  operators  can  be  optimized autom... see more

In this article we discuss a version of the Chebotarev density for function fields over perfect fields with procyclic absolute Galois groups. Our version of this density theorem differs from other versions in two aspects: we include ramified primes and we... see more

Random linear network coding (RLNC) can greatly aid data transmission in lossy wireless networks. However, RLNC requires computationally complex matrix multiplications and inversions in finite fields (Galois fields). These computations are highly demandin... see more

We give an explicit proof of the fundamental theorem of Grothendieck Galois theory: the category of separable algebras over a field K is anti-equivalent to the category of continuous actions on finite sets of the profinite fundamental group of K.

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