نتایج جستجو برای: finite fields
تعداد نتایج: 486937 فیلتر نتایج به سال:
Let F be a finite field, and 4: F* + E a surjective group homomorphism from the multiplicative group F* of F to a non-trivial abelian group E. A theorem of McConnel (Acta Arith. 8 (1963) 127-151) describes the permutations e of F with the property that d(ux uy) = d(x y) for all X, j’ E F, .Y #J. We give a short proof of this theorem, based on an argument of Bruen and Levinger (Canad. J. Math. 2...
The problem of a computationally feasible method of finding the discrete logarithm in a (large) finite field is discussed, presenting the main algorithms in this direction. Some cryptographic schemes based on the discrete logarithm are presented. Finally, the theory of linear recurring sequences is outlined, in relation to its applications in cryptology.
There are lots of results on the “random-like” behaviour of square elements in finite fields. For example, they can be used in combinatorial constructions and algorithms, as their properties somehow “imitate” a random distribution. In this paper we investigate the more general question concerning the behaviour of d-th powers in finite fields (where d is a fixed value). Surprisingly, they are di...
We have learnt about groups, rings, integral domains and fields till now. Fields have the maximum required properties and hence many nice theorems can be proved about them. For instance, in previous lectures we saw that the polynomials with coefficients from fields have unique factorization theorem. One of the important sub case of fields is when they are finite. In this case the fields can be ...
The category of motives over the algebraic closure of a finite field is known to be a semisimple Q-linear Tannakian category, but unless one assumes the Tate conjecture there is little further one can say about it. However, once this conjecture is assumed, it is possible to give an almost entirely satisfactory description of the category together with its standard fibre functors. In particular ...
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