A class of algebraic-exponential congruences modulo .
A class of permutation trinomials over finite fields
Let q > 2 be a prime power and , where . We prove that f is a permutation polynomial of if and only if one of the following occurs: (i) q is even and ; (ii) q ≡ 1 (mod 8) and t² = -2.
A fuzzy commitment scheme with McEliece's cipher.
A generalization of a theorem of Carlitz.
A generalization of Gauss sums and its applications to Siegel modular forms and L-functions associated with the vector space of quadratic forms.
A geometric characterization of the generators in a quadratic extension of a finite field
A geometric characterization of the generators in an extension of odd prime order of a finite field
A Goldbach theorem for polynomials of low degree over odd finite fields
À la recherche de petites sommes d'exponentielles
Soit une fraction rationnelle à coefficients entiers, vérifiant des hypothèses assez générales. On prouve l’existence d’une infinité d’entiers , ayant exactement deux facteurs premiers, tels que la somme d’exponentielles soit en , où est une constante ne dépendant que de la géométrie de . On donne aussi des résultats de répartition du type Sato-Tate, pour certaines sommes de Salié, modulo , avec entier comme ci- dessus.
A large family of Boolean functions
In a series of papers many Boolean functions with good cryptographic properties were constructed using number-theoretic methods. We construct a large family of Boolean functions by using polynomials over finite fields, and study their cryptographic properties: maximum Fourier coefficient, nonlinearity, average sensitivity, sparsity, collision and avalanche effect.
A lower bound theorem in Fq[x].
A matrix paraphrase of cyclotomy
A method for solving equations in finite fields
A new approach to the ElGamal encryption scheme
The ElGamal encryption scheme can be used for both digital signatures and encryption, and its security results from the difficulty of calculating discrete logarithms in a finite field. This algorithm usually works in a multiplicative group of GF(p) and in this case the progress in the discrete logarithm problem forces the users of such a basic ElGamal public key cryptosystem to permanently increase a prime modulus p in order to ensure the desired security. But the task of finding a multiplicative...
A new cubic character sum
A note on evaluations of some exponential sums
1. Introduction. The recent article [1] gives explicit evaluations for exponential sums of the form where χ is a non-trivial additive character of the finite field , odd, and . In my dissertation [5], in particular in [4], I considered more generally the sums S(a,N) for all factors N of . The aim of the present note is to evaluate S(a,N) in a short way, following [4]. We note that our result is also valid for even q, and the technique used in our proof can also be used to evaluate certain...
A note on exponential sums.
A note on Waring's problem in finite fields
A note on Waring's problem in GF (p)
A note on weight enumerators of linear self-dual codes.