Using the Kummer surface, we generalize Montgomery ladder for scalar multiplication to the Jacobian of genus 2 curves in characteristic 2. Previously this method was known for elliptic curves and for genus 2 curves in odd characteristic. We obtain an algorithm that is competitive compared to usual methods of scalar multiplication and that has additional properties such as resistance to side-cha...

We present an algorithm for computing the cardinality of the Jacobian of a random Picard curve over a finite field. If the underlying field is a prime field Fp, the algorithm has complexity O( √ p).

We introduce the twisted μ4-normal form for elliptic curves, deriving in particular addition algorithms with complexity 9M+ 2S and doubling algorithms with complexity 2M + 5S + 2m over a binary field. Every ordinary elliptic curve over a finite field of characteristic 2 is isomorphic to one in this family. This improvement to the addition algorithm, applicable to a larger class of curves, is co...

This paper presents a novel progressive surface modelling method to construct a freeform surface incrementally based on 3D motion sketches that represent the boundary and interior characteristic curves. The approach can construct a base surface model from multiple boundary curves and support incremental surface updating from interior characteristic curves which may cross the boundary curves or ...

We develop a mixed-characteristic version of the MoriMukai technique for producing rational curves on K3 surfaces. We reduce modulo p, produce rational curves on the resulting K3 surface over a finite field, and lift to characteristic zero. As an application, we prove that all complex K3 surfaces with Picard group generated by a class of degree two have an infinite number of rational curves.

Boosting is one of the most popular methods for constructing ensembles. The objective of this work is to present a boosting algorithm for regression based on the Regressor-Boosting algorithm, in which we propose the use of REC curves in order to select a good threshold value, so that only residuals greater than that value are considered as errors. The algorithm was empirically evaluated and its...

Let C be a supersingular genus-2 curve over an algebraically closed field of characteristic 3. We show that if C is not isomorphic to the curve y = x + 1 then up to isomorphism there are exactly 20 degree-3 maps φ from C to the elliptic curve E with j-invariant 0. We study the coarse moduli space of triples (C, E, φ), paying particular attention to questions of rationality. The results we obtai...

In this paper, we revisit the problem of computing the kernel of a separable isogeny of degree ` between two elliptic curves defined over a finite field Fq of characteristic p. We describe an algorithm the asymptotic time complexity of which is equal to e O(`(1 + `/p) log q) bit operations. This algorithm is particularly useful when ` > p and as a consequence, we obtain an improvement of the co...

In this note we extend the well-known binormal model via implementation of the epsilon-skew-normal (ESN) distribution developed by Mudholkar and Hutson (2000). We derive the equation for the receiver operating characteristic (ROC) curve assuming epsilon-skew-binormal (ESBN) model and examine the behavior of the maximum likelihood estimates for estimating the ESBN parameters. We then summarize t...

It is shown that the commutator subgroup of the fundamental group of a smooth irreducible affine curve over an uncountable algebraically closed field k of positive characteristic is a profinite free group of rank equal to the cardinality of k.