The purpose of this paper is to study the Hodge-Arakelov theory of elliptic curves (cf. [Mzk1-4]) in positive characteristic. The first two §’s (§1,2) are devoted to studying the relationship of the Frobenius and Verschiebung morphisms of an elliptic curve in positive characteristic to the Hodge-Arakelov theory of elliptic curves. We begin by deriving a “Verschiebung-Theoretic Analogue of the H...

The accurate medical diagnostic of a disease condition is fundamental for a correct medical decision. Disease screening programs are based, in general, in diagnostic tests which provide a binary response: a subject is classified as positive, if the test result is above a given threshold, and negative, otherwise. Therefore, false positive and false negative classifications can be generated. The ...

Characteristic polarization state theory is restudied for the symmetric coherent Sinclair scattering matrix case. First, the geometric relations of the characteristic polarization states on the Poincaré sphere are derived. Based on these relations, simple formulas are given for all of the characteristic polarization states of this Sinclair matrix in Stokes vector form. From the formulation, it ...

Measures including sensitivity, specificity, and positive and negative predictive values have been traditionally used to assess a diagnostic test's ability to detect the presence or absence of disease. Receiver operating characteristic (ROC) curve analysis allows visual evaluation of the trade-offs between sensitivity and specificity associated with different values of the test result, or diffe...

The paper is about the discrete logarithm problem for elliptic curves over characteristic 2 finite fields F2n of prime degree n. We consider practical issues about index calculus attacks using summation polynomials in this setting. The contributions of the paper include: a choice of variables for binary Edwards curves (invariant under the action of a relatively large group) to lower the degree ...

Let ĒΓ be a family of hyperelliptic curves over F cl 2 with general Weierstrass equation given over a very small field F. We describe in this paper an algorithm for computing the zeta function of Ēγ̄, with γ̄ in a degree n extension field of F, which has as time complexity Õ(n3) bit operations and memory requirements O(n2) bits. With a slightly different algorithm we can get time O(n2.667) and me...

We study methods for constructing confidence intervals, and confidence bands, for estimators of receiver operating characteristics. Particular emphasis is placed on the way in which smoothing should be implemented, when estimating either the characteristic itself or its variance. We show that substantial undersmoothing is necessary if coverage properties are not to be impaired. A theoretical an...

In hyperelliptic curve cryptography, finding a suitable hyperelliptic curve is an important fundamental problem. One of necessary conditions is that the order of its Jacobian is a product of a large prime number and a small number. In the paper, we give a probabilistic polynomial time algorithm to test whether the Jacobian of the given hyperelliptic curve of the form Y 2 = X+uX+vX satisfies the...