Separable Degree of the Gauss Map and Strict Dual Curves Over Finite Fields

Strict avalanche criterion over finite fields

Boolean functions on GF (2) which satisfy the Strict Avalanche Criterion (SAC) play an important role in the art of information security. In this paper, we extend the conception SAC to finite fields GF (p). A necessary and sufficient condition is given by using spectral analysis. Also, based on an interesting permutation polynomial theorem, we prove various facts about (n − 1)-th order SAC func...

Elliptic Curves over Finite Fields

In this chapter, we study elliptic curves defined over finite fields. Our discussion will include the Weil conjectures for elliptic curves, criteria for supersingularity and a description of the possible groups arising as E(Fq). We shall use basic algebraic geometry of elliptic curves. Specifically, we shall need the notion and properties of isogenies of elliptic curves and of the Weil pairing....

Pure Gauss Sums over Finite Fields

New classes of pairs e,p are presented for which the Gauss sums corresponding to characters of order e over finite fields of characteristic p are pure, i.e., have a real power. Certain pure Gauss sums are explicitly evaluated. §

Elliptic Curves over Finite Fields

Counting curves over finite fields

Article history: Received 25 August 2014 Received in revised form 10 September 2014 Accepted 18 September 2014 Available online 4 November 2014 Communicated by H. Stichtenoth MSC: 11G20 10D20 14G15 14H10