In this paper we combine the residue number system (RNS) representation and the leakresistant arithmetic on elliptic curves. These two techniques are relevant for implementation of elliptic curve cryptography on embedded devices. It is well known that the RNS multiplication is very efficient whereas the reduction step is costly. Hence, we optimize formulae for basic operations arising in leak-r...

We consider perturbations of integrable, area preserving non-twist maps of the annulus (those are maps that violate the twist condition in a very strong sense: @q 0 =@p changes sign). These maps appear in a variety of applications, notably transport in atmospheric Rossby waves. We show in suitable 2-parameter families the persistence of critical circles (invariant circles whose rotation number ...

We consider perturbations of integrable, area preserving non-twist maps of the annulus (those are maps in which the twist condition changes sign). These maps appear in a variety of applications, notably transport in atmospheric Rossby waves. We show in suitable 2-parameter families the persistence of critical circles (invariant circles whose rotation number is the maximum of all the rotation nu...

We consider perturbations of integrable area preserving non twist maps of the annulus those are maps in which the twist condition changes sign These maps appear in a variety of applications notably transport in atmospheric Rossby waves We show in suitable parameter families the persistence of critical circles invariant circles whose rotation number is the maximum of all the rotation numbers of ...

Recently, many papers have begun to consider so-called non-QRT birational maps of the plane. Compared to the QRT family of maps which preserve each biquadratic curve in a fibration of the plane, non-QRT maps send a biquadratic curve to another biquadratic curve belonging to the same fibration or to a biquadratic curve from a different fibration of the plane. In this communication, we give the g...

We consider a family of smooth maps on an infinite cylinder which have invariant curves that are nowhere smooth. Most points on such a curve are buried deep within its spiked structure, and the outermost exposed points of the curve constitute an invariant subset which we call the "facade" of the curve. We find that for surprisingly many of the maps in the family, all points in the facades of th...

We sharpen the two main tools used to treat the compactified Jacobian of a singular curve: Abel maps and presentation schemes. First we prove a smoothness theorem for bigraded Abel maps. Second we study the two complementary filtrations provided by the images of certain Abel maps and certain presentation schemes. Third we study a lifting of the Abel map of bidegree (m, 1) to the corresponding p...

A neural network method (SPINE-2D) is introduced to provide a sequence-based prediction of residue-residue contact maps. This method is built on the success of SPINE in predicting secondary structure, residue solvent accessibility, and backbone torsion angles via large-scale training with overfit protection and a two-layer neural network. SPINE-2D achieved a 10-fold cross-validated accuracy of ...