We prove a necessary condition for some polynomials of Gold and Kasami degree to be APN over Fqn for large n.

We prove a necessary condition for some polynomials of Kasami degree to be APN over Fqn for large n.

Let E be an elliptic curve defined over Fq, the finite field of q elements. We show that for some constant η > 0 depending only on q, there are infinitely many positive integers n such that the exponent of E(Fqn), the group of Fqn-rational points on E, is at most q exp ( −n log logn ) . This is an analogue of a result of R. Schoof on the exponent of the group E(Fp) of Fp-rational points, when a...

A method is given for constructing elements in Fqn whose orders are larger than any polynomial in n when n becomes large. As a by-product a theorem on multiplicative independence of compositions of polynomials is proved.

(1) s(k) = { vk if k ≤ n , ∑n−1 i=0 ais(k − n+ i) if k > n . We note that the elements of the sequence S can be considered as elements of the field Fqn which is an n-dimensional vector space over Fq. It is easy to see that without loss of generality we can suppose that f(0) 6= 0. Thus, it is possible to define the order of f , denoted by τ , as the least positive integer t for which f(x) divide...

Inmany applications, the cumulative distribution function (cdf) FQN of a positively weighted sum of N i.i.d. chi-squared randomvariables QN is required.Although there is no known closed-form solution for FQN , there are many good approximations. When computational efficiency is not an issue, Imhof’smethod provides a good solution. However, when both the accuracy of the approximation and the spe...

Let Fq denote the finite field of q elements, q = p r for prime p and positive integer r. A monic polynomial f(x) = x+ ∑n i=1 fix n−i ∈ Fq[x] is called a primitive polynomial if it is irreducible over Fq and any of the roots of f can be used to generate the multiplicative group Fqn of Fqn . Equivalently, f is primitive if the smallest positive integer w such that f(x) | x − 1 is w = q − 1. Prim...