In this paper we propose an improved algorithm for finding roots of polynomials over finite fields. This makes possible significant speed up of the decoding process of BCH, Reed-S...
In this paper we construct constant dimension codes with prescribed minimum distance. There is an increased interest in subspace codes in general since a paper [13] by K
We study the complexity of deciding whether a given homogeneous multivariate polynomial has a nontrivial root over a finite field. Given a homogeneous algebraic circuit C that com...
In this article we offer guidelines for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm based cryptosystems both over finite fields and over...
In hardware implementation for the finite field, the use of normal basis has several advantages, especially the optimal normal basis is the most efficient to hardware implementati...
Chang Han Kim, Yongtae Kim, Sung Yeon Ji, IlWhan P...
Public-key cryptosystems generally involve computation-intensive arithmetic operations, making them impractical for software implementation on constrained devices such as smart ca...
We introduce an efficient way of performing polynomial multiplication in a class of finite fields GF(pm ) in the frequency domain. The Fast Fourier Transform (FFT) based frequency...
Abstract. There are numerous subexponential algorithms for computing discrete logarithms over certain classes of finite fields. However, there appears to be no published subexponen...
We give estimates for exponential sums over finite fields in several variables. We study the case where the phase is either quadratic or more generally invariant under the action ...
In 1986, following the work of Schoof on counting points on elliptic curves over finite fields, new algorithms for primality proving emerged, due to Goldwasser and Kilian on the on...