The self-organization rule of planar neural networks has been proposed for learning of 2D distributions. However, it cannot be applied to 3D objects. In this paper, we propose a new model for global representation of the 3D objects. Based on this model, global topology reserving self-organization is achieved using parallel local competitive learning rule such as Kohonen's maps. The proposed model is able to represent the objects distributively and easily accommodate local features.

This paper first presents robust algorithms to extract invariants of the linear Lie algebra model from 3D objects. In particular, an extended 3D Hough transform is presented to extract accurate estimates of the normal vectors. The Least square fitting is used to find normal vectors and representation matrices. Then an algorithm of segmentation for 3D objects is shown using the invariants of the linear Lie algebra. Distributions of invariants, both in the invariant space and on the object surface, are used for clustering and edge detection.

Genus 3 hyperelliptic curve cryptosystems are capable of fast-encryption on a 64-bit CPU, because a 56-bit field is enough for their definition fields. Recently, Kuroki et al. proposed an extension of the Harley algorithm, which had been known as the fastest addition algorithm of divisor classes on genus 2 hyperelliptic curves, on genus 3 hyperelliptic curves and Pelzl et al. improved the algorithm. This paper shows an improvement of the Harley algorithm on genus 3 hyperelliptic curves using Toom's multiplication. The proposed algorithm takes only I + 70M for an addition and I + 71M for a doubling instead of I + 76M and I + 74M respectively, which are the best possible of the previous works, where I and M denote the required time for an inversion and a multiplication over the definition field respectively. This paper also shows 2 variations of the proposed algorithm in order to adapt the algorithm to various platforms. Moreover this paper discusses finite field arithmetic suitable for genus 3 hyperelliptic curve cryptosystems and shows implementation results of the proposed algorithms on a 64-bit CPU. The implementation results show a 160-bit scalar multiplication can be done within 172 µs on a 64-bit CPU Alpha EV68 1.25 GHz.

The Weil descent attack, suggested by Frey, has been implemented by Gaudry, Hess and Smart (the so-called GHS attack) on elliptic curves over finite fields of characteristic two and with composite extension degrees. Recently, Diem presented a general treatment of the GHS attack to hyperelliptic curves over finite fields of arbitrary odd characteristics. This paper shows that Diem's approach can be extended to curves of which the function fields are cyclic Galois extensions. In particular, we show the existence of GHS Weil restriction, triviality of the kernel of GHS conorm-norm homomorphism, and lower/upper bounds of genera of the resulting curves.

This note presents a new global optimization method and derives a learning schema based on the method for multilayer artificial neural networks. The schema consists of (1) pasting" the admissible region in Rn to a n-D torus Tn and smoothly connecting the potential function at the boundary; (2) global searching along the flow of a nonvanishing vector field on the compact smooth manifold Tn. This flow is featured by the ability of automatically passing through distinct local minima one after another along the negative/positive gradient field. It has also a unit norm everywhere on the Tn, so the searching speed will not slow down in the neighborhood of critical points.

Uniform color spaces are very important in color engineering, image source coding and multimedia information processing. In spite of many efforts have been paid on the subject, however, construction of an exact uniform color space seems difficult until now. Existing approaches mainly used local and heuristic approximations. Moreover, there seemed also certain confusion in definitions of the uniform spaces. In this paper we discuss the issue from a point of view of global Riemannian geometry. The equivalence between global and local definitions of uniform space are shown. Then both an exact and a simplified algorithm are presented to uniformize either a part or the totality of a color space. These algorithms can be expected to find applications in optimal quantization of color information.

In this paper, a new method for canceling the interchannel interference in the presence of crosstalk is proposed. The cancellation problem is formulated as a system identification problem, and then the transmission path and the interference path of each channel are estimated with the Recursive Prediction Error Method. IIR adaptive filters are used to implement interference cancelers. In addition, this method is shown to be able to apply to the noise canceling problem. The performance of the new method is verified by computer simulations.

Counting the number of points of Jacobian varieties of hyperelliptic curves over finite fields is necessary for construction of hyperelliptic curve cryptosystems. Recently Gaudry and Harley proposed a practical scheme for point counting of hyperelliptic curves. Their scheme consists of two parts: firstly to compute the residue modulo a positive integer m of the order of a given Jacobian variety, and then search for the order by a square-root algorithm. In particular, the parallelized Pollard's lambda-method was used as the square-root algorithm, which took 50CPU days to compute an order of 127 bits. This paper shows a new variation of the baby step giant step algorithm to improve the square-root algorithm part in the Gaudry-Harley scheme. With knowledge of the residue modulo m of the characteristic polynomial of the Frobenius endomorphism of a Jacobian variety, the proposed algorithm provides a speed up by a factor m, instead of in square-root algorithms. Moreover, implementation results of the proposed algorithm is presented including a 135-bit prime order computed about 15 hours on Alpha 21264/667 MHz and a 160-bit order.