Jinhui Chao

An Improved Baby Step Giant Step Algorithm for Point Counting of Hyperelliptic Curves over Finite Fields

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 algorithm for point counting of hyperelliptic curves. Their algorithm consists of two parts: firstly to compute the residue modulo an 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 Pollards 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 algorithm. 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 ?m in square-root algorithms. Moreover, implementation results of the proposed algorithm is presented including a 135-bit prime order computed in 16 hours on Alpha 21264/667MHz.

Design of Elliptic Curves with Controllable Lower Boundary of Extension Degree for Reduction Attacks

In this paper, we present a design strategy of elliptic curves whose extension degrees needed for reduction attacks have a controllable lower boundary, based on the complex multiplication fields method of Atkin and Morain over prime fields.

Cubical singular simplex model for 3D objects and fast computation of homology groups

This paper proposes a new simplex model for 3D objects: a cubical singular simplex model instead of the traditional triangularization simplex model. An extended Kohonen mapping is then presented as an efficient learning rule of the model. Based on this model, one can derive a pyramid structure for multi-resolution hierarchy, which is not possible for triangularization simplex. Besides, a fast algorithm is shown to calculate the homology groups of the objects as topological invariants from the proposed model.

Construction of Secure Elliptic Cryptosystems Using CM Tests and Liftings

Elliptic curves over number fields with CM can be used to design non-isogenous elliptic cryptosystems over finite fields efficiently. The existing algorithm to huild such CM curves, so-called the CM field algorithm, is based on analytic expansion of modular functions, costing computations of O(2 5h/2 h 21/4 ) where h is the class number of the endomorphism ring of the CM curve. Thus it is effective only in the small class number cases. This paper presents polynomial time algorithms in h to build CM elliptic curves over number fields. In the first part, probabilistic probabilistic algorithms of CM tests are presented to find elliptic curves with CM without restriction on class numbers. In the second part, we show how to construct ring class fields from ray class fields. Finally, a deterministic algorithm for lifting the ring class equations from small finite fields thus construct CM curves is presented. Its complexity is shown as O(h 7 ).

A new configuration for echo canceller adaptable during double talk periods

A three-port echo canceler (EC) configuration is proposed which observes the signal of the near-end side on a two-wire circuit in addition to the four-wire circuit signals. Embedding these signals on hybrid ports into a three-dimensional autoregressive process, echo path and innovations of near- and far-end speeches can be estimated through a three-channel lattice filter. The new configuration is then able to track echo path time variance, even during double talk (DT), and requires no changeover at either the beginning or end of DT, thus eliminating the need for DT detection. Two echo synthesizers utilizing inverse lattice and the echo path estimate possess guaranteed stability without the need for testing. >

A New ID-Based Key Sharing System

Non-interactive ID-based key sharing schemes are convenient in practice since they do not need prehminary communication. However, they are vulnerable to entities conspiracy. This paper proposes a new ID-based non-interactive key sharing scheme with high security against conspiracy of entities.

A stable and distortion-free IIR echo and howling canceler

The authors propose a configuration for an infinite impulse response (IIR) adaptive echo and howling canceller, which consists of a two-channel maximum entropy lattice filter and its inverse filter. The echo is canceled by the adaptive lattice filter, while the signal distortion is eliminated by the inverse lattice. With stability guaranteed without the necessity of testing, the structure costs O(N) multiplications per sampling period. The algorithm can also be greatly simplified for white input cases. >

A fast adaptive filter algorithm using eigenvalue reciprocals as stepsizes

It is shown that there exist finite optimum update positions in the gradient direction of the least-mean-square (LMS) algorithm. The optimum stepsizes to reach these positions are in a discrete set. On this basis, a new adaptive filter (ADF) algorithm is proposed. The discrete cosine transform, a fairly good approximation of the Karhunen-Loeve transform for a large number of signal classes, is used to estimate the optimum stepsizes. A block-averaging operation is also used for smoothing the gradient estimate. Computer simulations show that the proposed ADF algorithm provides fast convergence rates when the input signal autocorrelation matrix has either large or small eigenvalue spread (ratio of the largest to the smallest eigenvalues). The number of multiplications required by the new ADF is about 11 log/sub 2/ (N)+12, which is comparable to the 10 log/sub 2/ (N)+8 required by the fast LMS algorithm. >

Color Reproduction Using Riemann Normal Coordinates

In this paper we use tools from Riemann geometry to construct color reproduction methods that take into account the varying color perception properties of observers. We summarize the different steps in the processing: the estimation of the discrimination thresholds, the estimation of the Riemann metric, the construction of the metric-preserving or color-difference-preserving mapping and the usage of Semantic Differentiation (SD) techniques in the evaluation. We tested the method by measuring the discrimination data for 45 observers. We illustrate the geometric properties of the color spaces obtained and show the result of the metric-preserving maps between the color space of color-normal observers and a color-weak observer. We then apply the obtained maps to produce color corrected reproductions of two natural images.

A new IIR adaptive echo canceler: GIVE

A novel IIR adaptive gradient instrumental variable echo canceler (GIVE) is presented. Its features include adaptive controllability during double-talk periods in acoustic conference systems; guarantee of global convergence; low computational cost (the same order as the IIR LMS algorithm of the equation error method); and flexible structures (parallel or series-parallel structures). We also show a convergence analysis for gradient adaptive algorithms including GIVE. Based on this analysis, the optimum stepsize for GIVE and three suboptimum algorithms are proposed to accelerate convergence and reduce misadjustment. In addition, a simple method that guarantees the stability of IIR filters and a configuration of GIVE applicable to closed loop systems are presented. These proposals are extensively studied by computer simulations. >