The MOV and FR algorithms, which are representative attacks on elliptic curve cryptosystems, reduce the elliptic curve discrete logarithm problem (ECDLP) to the discrete logarithm problem in a finite field. This paper studies these algorithms and introduces the following three results. First, we show an explicit condition under which the MOV algorithm can be applied to non-supersingular ellipti...

In this paper, a model of self-organizing spiking neural networks is introduced and applied to mobile robot environment representation and path planning problem. A network of spike-response-model neurons with a recurrent architecture is used to create robot’s internal representation from surrounding environment. The overall activity of network simulates a self-organizing system with unsupervise...

Integration of system process information obtained through an image processing system with an evolving knowledge database to improve the accuracy and predictability of wear particle analysis is the main focus of the paper. The objective is to automate intelligently the analysis process of wear particle using classification via self organizing maps. This is achieved using relationship measuremen...

In recent years there has been much interest in the development and the fast computation of bilinear pairings due to their practical and myriad applications in cryptography. Well known efficient examples are the Weil and Tate pairings and their variants such as the Eta and Ate pairings on the Jacobians of (hyper-)elliptic curves. In this paper, we consider the use of projective coordinates for ...

Explicit congruences (mod p) are proved for the class equations or the products of class equations corresponding to discriminants D = −8p,−3p, −12p in the theory of complex multiplication, where p is an odd prime. These congruences are used to give a new proof of a theorem of Ogg, which states that there are exactly 15 primes p for which all j-invariants of supersingular elliptic curves in char...

One of the most growing areas in the embedded community is multimedia devices. Multimedia devices incorporate a number of complicated functions for their operation, like motion estimation. A multitude of different implementations have been proposed to reduce motion estimation complexity, such as spiral search. We have studied the implementations of spiral search and identified areas of improvem...

Let L be a number field and let E/L be an elliptic curve with potential supersingular reduction at a prime ideal ℘ of L above a rational prime p. In this article we describe a formula for the slopes of the Newton polygon associated to the multiplication-by-p map in the formal group of E, that only depends on the congruence class of p mod 12, the ℘-adic valuation of the discriminant of a model f...