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Koblitz, Solinas, and others investigated a family of elliptic curves which admit faster cryptosystem computations. In this paper, we generalize their ideas to hyperelliptic curves of genus 2. We consider the following two hyperelliptic curves Cα : v 2 + uv = u 5 + α u 2 + 1 defined over F2 with α = 0, 1, and show how to speed up the arithmetic in the Jacobian JC α (F2n) by making use of the Frobenius automorphism. With two precomputations, we are able to obtain a speed-up by a factor of 5.5 compared to the generic double-and-add-method in the Jacobian. If we allow 6 precomputations, we are even able to speed up by a factor of 7.

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Abstract. A Littlewood polynomial is a polynomial in C[z] having all of its coefficients in {−1, 1}. There are various old unsolved problems, mostly due to Littlewood and Erdős, that ask for Littlewood polynomials that provide a good approximation to a function that is constant on the complex unit circle, and in particular have small L q norm on the complex unit circle. We consider the Fekete polynomialswhere p is an odd prime and ( · | p) is the Legendre symbol (so that z −1 fp(z) is a Littlewood polynomial). We give explicit and recursive formulas for the limit of the ratio of L q and L 2 norm of fp(z) when q is an even positive integer and p → ∞. To our knowledge, these are the first results that give these limiting values for specific sequences of nontrivial Littlewood polynomials and infinitely many q. Similar results are given for polynomials obtained by cyclically permuting the coefficients of Fekete polynomials and for Littlewood polynomials whose coefficients are obtained from additive characters of finite fields. These results vastly generalise earlier results on the L 4 norm of these polynomials.

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This paper is devoted to the study of extended multicriteria location problems, which are obtained from a given planar single-facility multicriteria location problem with respect to the maximum norm by adding new cost functions. By means of an appropriate decomposition approach, we develop an implementable algorithm for generating an efficient solution of such extended problems.