In this paper, we compute -isogenies between abelian varieties over a field of characteristic different from 2 in polynomial time in , when is an odd prime which is coprime to the characteristic. We use level n symmetric theta structure where n = 2 or n = 4. In a second part of this paper we explain how to convert between Mumford coordinates of Jacobians of genus 2 hyperelliptic curves to theta coordinates of level 2 or 4. Combined with the preceding algorithm, this gives a method to compute ( , )-isogenies in polynomial time on Jacobians of genus 2 curves.

Control systems running on a computer are subject to timing disturbances coming from implementation constraints. Fortunately closed-loop systems behave robustly w.r.t. modelling errors and disturbances, and the controller design can be performed to explicitly enhance robustness against specific uncertainties. On one hand robustness in process controllers can be used to comply with weakly modelled timing uncertainties. On the other hand the principle of robust closed-loop control can also be applied to the real-time scheduler to provide on-line adaption of some scheduling parameters, with the objective of controlling the computing resource allocation. The control performance specification may be set according to both control and implementation constraints. The approach is illustrated through several examples using simulation and an experimental feedback scheduler is briefly described.

This brief deals with the adaptation of a real-time controller's sampling period to account for the available computing resource variations. The design of such controllers requires a parameter-dependent discrete-time model of the plant, where the parameter is the sampling period. A polytopic approach for linear parameter varying (LPV) systems is then developed to get an sampling period dependent controller. A reduction of the polytope size is here performed which drastically reduces the conservatism of the approach and makes easier the controller implementation. Some experimental results on a T-inverted pendulum are provided to show the efficiency of the approach.

We describe an efficient algorithm for the computation of separable isogenies between abelian varieties represented in the coordinate system given by algebraic theta functions. Let A be an abelian variety of dimension g defined over a field of odd characteristic. Our algorithm comprises two principal steps. First, given a theta null point for A and a subgroup K isotropic for the Weil pairing, we explain how to compute the theta null point corresponding to the quotient abelian variety A/K. Then, from the knowledge of a theta null point of A/K, we present an algorithm to obtain a rational expression for an isogeny from A to A/K. The algorithm that results from combining these two steps can be viewed as a higher-dimensional analog of the well-known algorithm of Vélu for computing isogenies between elliptic curves. In the case where K is isomorphic to (Z/ Z) g for ∈ N * , the overall time complexity of this algorithm is equivalent to O(log ) additions in A and a constant number of th root extractions in the base field of A. In order to improve the efficiency of our algorithms, we introduce a compressed representation that allows us to encode a point of level 4 of a g-dimensional abelian variety using only g(g + 1)/2 · 4 g coordinates. We also give formulas for computing the Weil and commutator pairings given input points in theta coordinates.