We develop efficient precomputation methods of multi-scalar multiplication on ECC. We should recall that multi-scalar multiplication is required in some elliptic curve cryptosystems including the signature verification of ECDSA signature scheme. One of the known fast computation methods of multi-scalar multiplication is a simultaneous method. A simultaneous method consists of two stages; precomputation stage and evaluation stage. Precomputation stage computes points of precomputation, which are used at evaluation stage. Evaluation stage computes multi-scalar multiplication using precomputed points. In the evaluation stage of simultaneous methods, we can compute the multi-scalar multiplied point quickly because the number of additions is small. However, if we take a large window width, we have to compute an enormous number of points in precomputation stage. Hence, we have to compute an abundance of inversions, which have large computational amount. As a result, precomputation stage requires much time, as well known. Our proposed method reduces from O(22w) inversions to O(w) inversions for a window width w, using Montgomery trick. In addition, our proposed method computes uP and vQ first, then compute uP+vQ, where P,Q are elliptic points. This procedure enables us to remove unused points of precomputation. Compared with the method without Montgomery trick, our proposed method is 3.6 times faster in the case of the precomputation stage for simultaneous sliding window NAF method with window width w=3 and 160-bit scalars under the assumption that I/M=30, S/M=0.8, where I,M,S respectively denote computational amounts of inversion, multiplication and squaring on a finite field.

Software obfuscation is a promising approach to protect intellectual property rights and secret information of software in untrusted environments. Unfortunately previous software obfuscation techniques share a major drawback that they do not have a theoretical basis and thus it is unclear how effective they are. Therefore we propose new software obfuscation techniques in this paper. The techniques are based on the difficulty of interprocedural analysis of software programs. The essence of our obfuscation techniques is a new complexity problem to precisely determine the address a function pointer points to in the presence of arrays of function pointers. We show that the problem is NP-hard and the fact provides a theoretical basis for our obfuscation techniques. Furthermore, we have already implemented a prototype tool that obfuscates C programs according to our proposed techniques and in this paper we describe the implementation and discuss the experiments results.

We introduce efficient algorithms for the τ-adic sliding window method, which is a scalar multiplication algorithm on Koblitz curves over F2m. The τ-adic sliding window method is divided into two parts: the precomputation part and the main computation part. Until now, there has been no efficient way to deal with the precomputation part; the required points of the elliptic curves were calculated one by one. We propose two fast algorithms for the precomputation part. One of the proposed methods decreases the cost of the precomputation part by approximately 30%. Since more points are calculated, the total cost of scalar multiplication is decreased by approximately 7.5%.

When we use an adaptive array antenna (AAA) with the minimum mean square error (MMSE) criterion under the multipath environment, where the receiving signal level varies, it is difficult for the AAA to converge because of the distortion of the desired wave. Then, we need the equalization both in space and time domains. A tapped-delay-line adaptive array antenna (TDL-AAA) and the AAA with linear equalizer (AAA-LE) have been proposed as simple space-temporal equalization. The AAA-LE has not utilized the recursive least square (RLS) algorithm. In this paper, we propose a space-temporal simultaneous processing equalizer (ST-SPE) that is an AAA-LE with the RLS algorithm. We proposed that the first tap weight of the LE should be fixed and the necessity of that is derived from a normal equation in the MMSE criterion. We achieved the space-temporal simultaneous equalization with the RLS algorithm by this configuration. The ST-SPE can reduce the computational complexity of the space-temporal joint equalization in comparison to the TDL-AAA, when the ST-SPE has almost the same performance as the TDL-AAA in multipath environment with minimum phase condition such as appeared at line-of-sight (LOS).

A siphon-trap of a Petri net N is defined as a place set S with S = S, where S = { u| N has an edge from u to a vertex of S} and S = { v| N has an edge from a vertex of S to v}. A minimal siphon-trap is a siphon-trap such that any proper subset is not a siphon-trap. The following polynomial-time algorithms are proposed: (1) FDST for finding, if any, a minimal siphon-trap or even a maximal class of mutually disjoint minimal siphon-traps of a given Petri net; (2) FDSTi that repeats FDST i times in order to extract more minimal siphon-traps than FDST. (3) STFM_T (STFM_Ti, respectively) which is a combination of the Fourier-Motzkin method and FDST (FDSTi) and which has high possibility of finding, if any, at least one minimal-support nonnegative integer invariant.

When solving combinatorial optimization problems with a binary Hopfield-type neural network, the updating process in neural network is an important step in achieving a solution. In this letter, we propose a new updating procedure in binary Hopfield-type neural network for efficiently solving combinatorial optimization problems. In the new updating procedure, once the neuron is in excitatory state, then its input potential is in positive saturation where the input potential can only be reduced but cannot be increased, and once the neuron is in inhibitory state, then its input potential is in negative saturation where the input potential can only be increased but cannot be reduced. The new updating procedure is evaluated and compared with the original procedure and other improved methods through simulations based on N-Queens problem. The results show that the new updating procedure improves the searching capability of neural networks with shorter computation time. Particularly, the simulation results show that the performance of proposed method surpasses the exiting methods for N-queens problem in synchronous parallel computation model.

Algorithms are presented for the four elementary arithmetic operations, to perform reliable floating-point arithmetic operations. These arithmetic operations can be achieved by applying residue techniques to the weighted number systems and performed with no accuracy lost in the process of the computing. The arithmetic operations presented can be used as elementary tools (on many existing architectures) to ensure the reliability of numerical computations. Simulation results especially for the solutions of ill-conditioned problems are given with emphasis on the practical usability of the tools.

This paper presents an efficient graph-based evolutionary optimization technique called Evolutionary Graph Generation (EGG) and its extension to a parallel version. A new version of parallel EGG system is based on a coarse-grained model of parallel processing and can synthesize heterogeneous networks of various different components efficiently. The potential capability of parallel EGG system is demonstrated through the design of current-mode logic circuits.

This letter treats computational complexity of bounded asymmetric choice (AC) net. AC net is a subclass of Petri net that properly includes the class of well-known extended free choice net. It is shown that satisfiability problem of Boolean expressions is polynomial time reducible to liveness problem of bounded AC nets. This implies that the problem is NP-hard.

This paper presents some new protocols for (M+1)st-price auction, a style of auction in which the highest M bidders win and pay a uniform price, determined by the (M+1)st price. A set of distributed servers collaborates to resolve the (M+1)st price without revealing any information in terms of bids including the winners' bids. A new trick to jointly and securely compute the highest value as a degree of distributed polynomials is introduced. The building block requires just one round for bidders to cast bids and one round for auctioneers to determine the winners.

This paper investigates the accepting powers of one-way alternating and deterministic multi-counter automata operating in realtime. We partially solve the open problem posed in [4], and show that for each k1, there is a language accepted by a realtime one-way deterministic (k+3)-counter automaton, but not accepted by any realtime one-way alternating k-counter automaton.

This paper develops a simple algorithm for calculating a polynomial curve or surface in a parallel way. The number of arithmetic operations and the necessary time for the calculation are evaluated in terms of polynomial degree and resolution of a curve and the number of processors used. We made some comparisons between our method and a conventional method for generating polynomial curves and surfaces, especially in computation time and approximation error due to the reduction of the polynomial degree. It is shown that our method can perform fast calculation within tolerable error.

The class NQP was proposed as the class of problems that are solvable by non-deterministic quantum Turing machines in polynomial time. In this paper, we introduce non-deterministic quantum finite automata in which the same non-determinism as in non-deterministic quantum Turing machines is applied. We compare non-deterministic quantum finite automata with the classical counterparts, and show that (unlike the case of classical finite automata) the class of languages recognizable by non-deterministic quantum finite automata properly contains the class of all regular languages.

We give an overview of the computational complexity of linear and mesh-connected cellular and iterative arrays with respect to well known models of sequential and parallel computation. We discuss one-way communication versus two-way communication, serial input versus parallel input, and space-efficient simulations. In particular, we look at the parallel complexity of cellular arrays in terms of the PRAM theory and its implications, e.g., to the parallel complexity of recurrence equations and loops. We also point out some important and fundamental open problems that remain unresolved. Next, we investigate the solvability of some reachability and safety problems concerning machines operating in parallel and cite some possible applications. Finally, we briefly discuss the complexity of the "commutativity analysis" technique that is used in the areas of parallel computing and parallelizing compilers.

In Chirp-Pulse Microwave Computed Tomography (CP-MCT) the images are affected by the blur which is inherent to the measurement principle and is described by a space-variant Point Spread Function (PSF). In this paper we investigate the PSF of CP-MCT including the space dependence both experimentally and computationally. The experimental evaluation is performed by measuring the projections of a target consisting of a thin low-loss dielectric rod surrounded by a saline solution and placed at various positions in the measuring region. On the other hand, the theoretical evaluation is obtained by computing the projections of the same target via a numerical solution of Maxwell's equations. Since CP-MCT uses a chirp signal, the numerical evaluation is carried out by the use of a FD-TD method. The projections of the rod could be obtained by computing the field during the sweep time of the chirp signal for each position of the receiving antenna. Since this procedure is extremely time consuming, we compute the impulse response function of the system by exciting the transmitting antenna with a wide-band Gaussian pulse. Then the signal transmitted in CP-MCT is obtained by computing the convolution product in time domain of the input chirp pulse with the impulse response function of the system. We find a good agreement between measured and computed PSF. The rationality of the computed PSF is verified by three distinct ways and the usefulness of this function is shown by a remarkable effect in the restoration of CP-MCT images. Knowledge on the space-variant PSF will be utilized for more accurate image deblurring in CP-MCT.

This paper describes how the symmetry of a three-phase circuit prevents the symmetric modes of several subharmonic oscillations. First, we make mathematically it clear that the generation of symmetrical 1/3l-subharmonic oscillations (l=1,2,) are impossible in the three-phase circuit. As far as 1/(3l+1)-subharmonic oscillations (l=1,2,) and 1/(3l+2)-subharmonic oscillations (l=0,1,) are concerned, the former in negative-phase sequence and the latter in positive-phase sequence are shown to be impossible. Further, in order to confirm the above results, we apply the method of interval analysis to the circuit equations and obtain all steady state solutions with unsymmetric modes.

This letter presents an efficient graph-based evolutionary optimization technique, and its application to the transistor-level design of multiple-valued arithmetic circuits. The key idea is to introduce "circuit graphs with colored terminals" for modeling heterogeneous networks of various components. The potential of the proposed approach is demonstrated through experimental synthesis of a radix-4 signed-digit (SD) full adder circuit.

Recently, an efficient algorithm has been proposed for finding all solutions of systems of nonlinear equations using inverses of approximate Jacobian matrices. In this letter, an effective technique is proposed for improving the computational efficiency of the algorithm with a little bit of computational effort.

Petri net is a mathematical model for concurrent systems. Liveness is one of important properties of Petri net. Liveness problem of general Petri net is of exponential space complexity and subclasses are suggested with less computational complexity. It is well known that liveness problem of bounded (extended) free choice net is solved in deterministic polynomial time. This paper treats liveness problem of AC/DC nets. AC/DC net is a subclass of Petri net that exhibits no confusion (mixture of concurrency and conflict). This class properly includes the class of free choice nets. It is shown that every minimal siphon of an AC/DC net is trap if and only if every strongly connected siphon is a trap. This result shows that monotone liveness of bounded AC/DC net is solved in deterministic polynomial time. It is shown that this result is true of bounded time AC/DC net with static fair condition.

The imprecise computation is one of the promising schemes in the real time systems to adapt quality of computations to change of load with keeping the deadlines of tasks in the systems. When overload occurs in the systems, the minimum requirements on the deadline are assured by decreasing quality of the computation. This paper describes how to apply the concept of the imprecise computation to automobile control in the expressway assuming the intelligent transportation system (shortly, ITS). The deadline violation of tasks for automobile control in the expressway induces collision of automobiles. Regardless of whether the expressway is congested or not, collision of automobiles must be avoided. To satisfy such requirement, the concept of the imprecise computation is effective. This paper proposes an adaptive scheduling using the imprecise computation to avoid collision of automobiles and increase throughput, and shows results of simulation experiments about an adaptive scheduling for automobiles control.