On the number of solutions of congruences and equations in
On the number of values taken by a polynomial over a finite field
On the number of zero trace elements in polynomial bases for F2n.
Let Fq denote the finite field of q elements. O. Ahmadi and A. Menezes have recently considered the question about the possible number of elements with zero trace in polynomial bases of F2n over F2. Here we show that the Weil bound implies that there is such a basis with n + O(log n) zero-trace elements.
On the -adic continuation of the logarithmic derivative of certain hypergeometric functions
On the pure Jacobi sums
On the quadriquadric Curve in connexion with the theory of Elliptic Functions
On the ranges of discrete exponentials.
On the restricted Waring problem over
1. Introduction. The Waring problem for polynomial cubes over a finite field F of characteristic 2 consists in finding the minimal integer m ≥ 0 such that every sum of cubes in F[t] is a sum of m cubes. It is known that for F distinct from ₂, ₄, , each polynomial in F[t] is a sum of three cubes of polynomials (see [3]). If a polynomial P ∈ F[t] is a sum of n cubes of polynomials in F[t] such that each cube A³ appearing in the decomposition has degree < deg(P)+3, we say that P is a restricted...
On the roots of the substitution Dickson polynomials.
On the set .
On the set of distances between two sets over finite fields.
On the special solutions of an equation in a finite field.
On the structure of finite rings
On the value set of small families of polynomials over a finite field, II
We obtain an estimate on the average cardinality (d,s,a) of the value set of any family of monic polynomials in of degree d for which s consecutive coefficients are fixed. Our estimate asserts that , where . We also prove that , where ₂(d,s,a) is the average second moment of the value set cardinalities for any family of monic polynomials of of degree d with s consecutive coefficients fixed as above. Finally, we show that , where ₂(d,0) denotes the average second moment for all monic polynomials...
On universal forms in finite fields
On Waring's problem in finite fields
On Waring's Problem in GF[p]
On zero-testing and interpolation of sums of characters.
Operations of Points on Elliptic Curve in Projective Coordinates
In this article, we formalize operations of points on an elliptic curve over GF(p). Elliptic curve cryptography [7], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security. We prove that the two operations of points: compellProjCo and addellProjCo are unary and binary operations of a point over the elliptic curve.