In this paper we propose a very simple and efficient encoding function from Fq to points of a hyperelliptic curve over Fq of the form H : y = f(x) where f is an odd polynomial. Hyperelliptic curves of this type have been frequently considered in the literature to obtain Jacobians of good order and pairing-friendly curves. Our new encoding is nearly a bijection to the set of Fq-rational points o...

Let d ≥ 1 be fixed. Let F be a number field of degree d, and let E/F be an elliptic curve. Let E(F )tors be the torsion subgroup of E(F ). In 1996, Merel proved the uniform boundedness conjecture, i.e., there is a constant B(d), which depends on d but not on the chosen field F or on the curve E/F , such that the size of E(F )tors is bounded by B(d). Moreover, Merel gave a bound (exponential in ...

The current methods of predictive controllers are utilized for those processes in which the rate of output variations is not high. For such processes, therefore, stability can be achieved by implementing the constrained predictive controller or applying infinite prediction horizon. When the rate of the output growth is high (e.g. for unstable nonminimum phase process) the stabilization seems to...

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...

In this paper, an effective sliding mode design is applied to chaos synchronization. The proposed controller can make the states of two identical modified Chua’s circuits globally asymptotically synchronized. Numerical results are provided to show the effectiveness and robustness of the proposed method. Keywords—Sliding mode, Chaos synchronization, Modified Chua’s circuit.

This Classifying Bird Sounds (chip notes) project’s purpose is to reduce the unwanted noise from recorded bird sound chip notes, design a scheme to detect differences and similarities between recorded chip notes, and classify bird sound chip notes. The technologies of determining the similarities of sound waves have been used in communication, sound engineering and wireless sound applications f...

This article presents a novel optimal pairing over supersingular genus-2 binary hyperelliptic curves. Starting from Vercauteren’s work on optimal pairings, we describe how to exploit the action of the 2-th power Verschiebung in order to further reduce the loop length of Miller’s algorithm compared to the genus-2 ηT approach. As a proof of concept, we detail an optimized software implementation ...

An ongoing challenge in cryptography is to find groups in which the DLP is computationally infeasible, that is, for which the best known attack is exponential in log(N). Such a group can be used as the setting for many cryptographic protocols, from Diffie-Hellman key exchange to El Gamal encryption ([14], 159). The most prominent example, first proposed in 1985, is a subgroup of points of an el...