Finite fields (Algebra)
Computing in Algebraic Closures of Finite Fields
... We present algorithms to construct and perform computations in algebraic closures of finite fields. Inspired by algorithms for constructing irreducible polynomials, our approach for con- structing closures ...
86
Modular Forms of Weight One Over Finite Fields
... a finite field into local pieces up to Galois ...over finite fields using modular symbols is ...for finite fields of characteristic p, from which we derive an algorithm for the ...
111
Lattice Models of Finite Fields
... Finite fields form an important chapter in abstract algebra, and mathematics in general, yet the traditional expositions, part of Abstract Algebra courses, focus on the axiomatic presentation, while ...
16
Some New Results about Trigonometry in Finite Fields
... Some New Results about Trigonometry in Finite Fields Amiri Naser*, Hasani Fysal Department of Mathematics, Payame Noor University, Tehran, Iran Received 26 December 2015; accepted 11 Jun[r] ...
5
On permutation polynomials over finite fields
... SCHMIDT, W.M., Equations Over Finite Fields, An Elementary Approach, Springer Lecture Notes, 536 1976..[r] ...
9
Several Classes of Permutation Polynomials over Finite Fields
... were first studied by Hermite [1] for the case of finite prime fields and by Dickson [4] for arbitrary finite fields. Permutation polynomials have been studied extensively and have important ...
7
On the Primitivity of Trinomials over Small Finite Fields
... and primitive trinomials have many important applications in the theory of finite fields, cryptography, and coding theory [2-4]. Hence, there are many results on the factorizations of trinomials and ...
6
Galois Groups of Polynomials and the Construction of Finite Fields
... The nature of polynomials of small degree was explored in [1], their general solutions were found which allow for the application of Galois ideas to analyse their splitting fields. The Galois groups of these ...
7
On elements of high order in general finite fields
... It is well known that the multiplicative group of a finite field is cyclic. A generator of the group is called a primitive element. The problem of constructing efficiently a primitive element for a given ...
6
On the set of distances between two sets over finite fields
... Rudnev, Erdös distance problem in vector spaces over finite fields, to appear in Transactions of the American Mathematical Society.. , Spherical averages, distance sets, and lattice poi[r] ...
5
A Versatile Multi-Input Multiplier over Finite Fields
... over finite fields is used extensively in multivariate public key cryptography and solving system of linear equations over finite ...over finite fields by using specific ...
8
Properties of sparse random matrices over finite fields
... Random matrices are ubiquitous in many branches of the natural sciences and mathematics ranging from biology to computer science, nuclear physics and quantum chaos. Activity in the area has been recently boosted by the ...
19
Multiplicative orders of elements in Conway's towers of finite fields
... use finite fields ...of finite field multiplicative group, it is not known how to rich the ...special finite fields [1, 3, 7, 12, ...
10
On Isogeny Graphs of Supersingular Elliptic Curves over Finite Fields
... [10] D. Kohel, “Endomorphism rings of elliptic curves over finite fields”, Ph.D. thesis, UC Berkeley, 1996. [11] C. Munuera and J. Tena, “An algorithm to compute the number of points on elliptic curves of ...
14
P schemes and Deterministic Polynomial Factoring Over Finite Fields
... In Chapter 3, we design a generic algorithm, which we refer to as the P -scheme algorithm , that deterministically factorizes f under GRH given f and f ˜ . The generic part of the algorithm is a subroutine that uses f ˜ ...
292
Cubic surfaces over finite fields
... In Chapter 5, for a cubic surface S defined over a finite field K and containing a K-line `, we introduce the c-invariants of S with respect to `. The c-invariants are integers that give information on the ...
104
Deterministic equation solving over finite fields
... desirable. Finite fields are also important in the classification of other combi- natorial objects, such as Hadamard matrices, difference sets, and finite affine and projective ...
96
Finding irreducible polynomials over finite fields
... fouiid in polvnomiil linic b^ niivc snrdi Ί(ιρ (ΐ\ is n«w ( tsil) si cn to bi rompiitiblc in.. pol>iH)iiuil tmR llif[r] ...
6
On the discrete logarithm problem in finite fields of fixed characteristic
... characteristic) fields of a certain form, relation generation for degree one elements runs in heuristic polynomial time, as does computing the logarithms of degree two elements using a technique which eliminates ...
20
On the matrix equation Xn=B over finite fields
... In this paper, we consider the problem of determining the number N Nn,m,B of the n-th roots in M of a given matrix.. Our present work generalizes a recent paper of the authors [1] in whi[r] ...
6