In this paper we classify curves of genus two over a perfect field k of characteristic two. We find rational models of curves with a given arithmetic structure for the ramification divisor and we give necessary and sufficient conditions for two models of the same type to be k-isomorphic. As a consequence, we obtain an explicit formula for the number of k-isomorphism classes of curves of genus t...

We describe a fast hash algorithm that maps arbitrary messages onto points of an elliptic curve defined over a finite field of characteristic 3. Our new scheme runs in time O(m) for curves over F3m . The best previous algorithm for this task runs in time O(m). Experimental data confirms the speedup by a factor O(m), or approximately a hundred times for practical m values. Our results apply for ...

We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first streaming algorithm for Euler characteristic curves. The usage of streaming removes the necessity to store the entire image in RAM. Experiments show that our im...

We present normal forms for elliptic curves over a field of characteristic 2 analogous to Edwards normal form, and determine bases of addition laws, which provide strikingly simple expressions for the group law. We deduce efficient algorithms for point addition and scalar multiplication on these forms. The resulting algorithms apply to any elliptic curve over a field of characteristic 2 with a ...

Let X be a projective curve of genus 2 over an algebraically closed field of characteristic 2. The Frobenius map on X induces a rational map on the moduli space of rank-2 bundles. We show that up to isomorphism, there is only one (up to tensoring by an order two line bundle) semi-stable vector bundle of rank 2 with determinant equal to a theta characteristic whose Frobenius pull-back is not sta...

We consider digital expansions of scalars for supersingular Koblitz curves in characteristic three. These are positional representations of integers to the base of τ , where τ is a zero of the characteristic polynomial T 2 ± 3T + 3 of a Frobenius endomorphism. They are then applied to the improvement of scalar multiplication on the Koblitz curves. A simple connection between τ -adic expansions ...

In his investigation on large K-automorphism groups of an algebraic curve, Stichtenoth obtained an upper bound on the order of the first ramification group of an algebraic curve X defined over an algebraically closed field of characteristic p. Stichtenoth’s bound has raised the problem of classifying all K-automorphism groups G of X with the following property: There is a point P ∈ X for which ...

In this paper we develop the theory of equisingular deformations of plane curve singularities in arbitrary characteristic. We study equisingular deformations of the parametrization and of the equation and show that the base space of its semiuniveral deformation is smooth in both cases. Our approach through deformations of the parametrization is elementary and we show that equisingular deformati...

We use a sequence of blow-ups over the projective space parametrizing plane curves of degree d to obtain some enumerative results concerning smooth plane curves of arbitrary degree. For d = 4 , this gives a first modem verification of results of H. G. Zeuthen. O. INTRODUCTION The kth 'characteristic number' of the d(dt3) -dimensional family of smooth plane curves of degree d, denoted Nd(k) in t...

Receiver operating characteristic curve is a standard method for reporting performance of a system. In this paper we show how to choose the optimal operating point when we are given a receiver operating curve, the prior probabilities, and the economic gain matrix. Unlike earlier methods, we make no assumptions regarding underlying distributions.