Arash Hariri

A new high dynamic range moduli set with efficient reverse converter

The Residue Number System (RNS) is a representation system which provides fast and parallel arithmetic. It has a wide application in digital signal processing and provides enhanced fault tolerance capabilities. In this work, we consider the 3-moduli set {2^n, 2^2^n-1, 2^2^n+1} and propose its residue to binary converter using the Chinese Remainder Theorem. We present its simple hardware implementation that is mainly composed of one Carry Save Adder (CSA), a 4n bit modulo 2^4^n-1 adder, and a few gates. We compare the performance and area utilization of our reverse converter to the reverse converters of the moduli sets { 2^n-1, 2^n, 2^n+1, 2^2^n+1} and {2^n-1, 2^n, 2^n+1, 2^n-2^(^n^+^1^)^/^2+1, 2^n+2^(^n^+^1^)^/^2+1} that have the same dynamic range and we demonstrate that our reverse converter is better in terms of performance and area utilization.

Bit-Serial and Bit-Parallel Montgomery Multiplication and Squaring over GF(2^m)

Multiplication and squaring are main finite field operations in cryptographic computations and designing efficient multipliers and squarers affect the performance of cryptosystems. In this paper, we consider the Montgomery multiplication in the binary extension fields and study different structures of bit-serial and bit-parallel multipliers. For each of these structures, we study the role of the Montgomery factor, and then by using appropriate factors, propose new architectures. Specifically, we propose two bit-serial multipliers for general irreducible polynomials, and then derive bit-parallel Montgomery multipliers for two important classes of irreducible polynomials. In this regard, first we consider trinomials and provide a way for finding efficient Montgomery factors which results in a low time complexity. Then, we consider type-II irreducible pentanomials and design two bit-parallel multipliers which are comparable to the best finite field multipliers reported in the literature. Moreover, we consider squaring using this family of irreducible polynomials and show that this operation can be performed very fast with the time complexity of two XOR gates.

A step forward in studying the compact genetic algorithm

The compact Genetic Algorithm (cGA) is an Estimation of Distribution Algorithm that generates offspring population according to the estimated probabilistic model of the parent population instead of using traditional recombination and mutation operators. The cGA only needs a small amount of memory; therefore, it may be quite useful in memory-constrained applications. This paper introduces a theoretical framework for studying the cGA from the convergence point of view in which, we model the cGA by a Markov process and approximate its behavior using an Ordinary Differential Equation (ODE). Then, we prove that the corresponding ODE converges to local optima and stays there. Consequently, we conclude that the cGA will converge to the local optima of the function to be optimized.

Digit-Serial Structures for the Shifted Polynomial Basis Multiplication over Binary Extension Fields

Finite field multiplication is one of the most important operations in the finite field arithmetic. Recently, a variation of the polynomial basis, which is known as the shifted polynomial basis, has been introduced. Current research shows that this new basis provides better performance in designing bit-parallel and subquadratic space complexity multipliers over binary extension fields. In this paper, we study digit-serial multiplication algorithms using the shifted polynomial basis. They include a Most Significant Digit (MSD)-first digit-serial multiplication algorithm and a hybrid digit-serial multiplication algorithm, which includes parallel computations. Then, we explain the hardware architectures of the proposed algorithms and compare them to their existing counterparts. We show that our MSD-first digit-serial shifted polynomial basis multiplier has the same complexity of the Least Significant Digit (LSD)-first polynomial basis multiplier. Also, we present the results for the hybrid digit-serial multiplier which offers almost the half of the latency of the best known digit-serial polynomial basis multipliers.

Letters: The Population-Based Incremental Learning Algorithm converges to local optima

Here, we propose a convergence proof for the Population-Based Incremental Learning (PBIL). First, we model the PBIL by a Markov process and approximate its behavior using an Ordinary Differential Equation (ODE). Then we prove that the corresponding ODE does not have any stable stationary point in the configuration space except the local maxima of the function to be optimized. Finally, we show that the ODE and consequently the PBIL converge to one of these stable points.

Concurrent Error Detection in Montgomery Multiplication over Binary Extension Fields

Multiplication is one of the most important operations in finite field arithmetic. It is used in cryptographic and coding applications, such as elliptic curve cryptography and Reed-Solomon codes. In this paper, we consider the finite field multiplication used in elliptic curve cryptography and design concurrent error detection circuits. It is shown in the literature that the Montgomery multiplication can be used in cryptography to accelerate the scalar multiplication. Here, we use a parity-based concurrent error detection approach to increase the reliability of different Montgomery multipliers available in the literature. First, we consider bit-serial Montgomery multiplication and propose an error detection circuit. Then, we apply the same technique on the digit-serial Montgomery multiplication. Finally, we consider low time-complexity bit-parallel Montgomery multiplication and design the required components to implement the concurrent error detection circuits. ASIC implementations have been completed to analyze the time and area overheads of the proposed schemes. Also, the error detection capability is investigated by software simulations. We show that our approach results in efficient error detection schemes with small time and area overheads.

A new fine-grained evolutionary algorithm based on cellular learning automata

In this paper a new evolutionary algorithm, called the CLA-EC (Cellular Learning Automata Based Evolutionary Computing), is proposed. This algorithm is a combination of evolutionary algorithms and the Cellular Learning Automata (CLA). In the CLA-EC each genome string in the population is assigned to one cell of the CLA, which is equipped with a set of learning automata. Actions selected by the learning automata of a cell determine the genome string for that cell. Based on a local rule, a reinforcement signal vector is generated and given to the set of learning automata residing in the cell. Each learning automaton in the cell updates its internal structure according to a learning algorithm and the received signal vector. The processes of action selection and updating the internal structures of learning automata are repeated until a predetermined criterion is met. To show the efficiency of the proposed model, to solve several optimization problems including real valued function optimization and data clustering problems.

A Convergence Proof for the Population Based Incremental Learning Algorithm

Here we propose a convergence proof for the population based incremental learning (PBIL). In our approach, first, we model the PBIL by the Markov process and approximate its behavior using Ordinary Differential Equation (ODE). Then we prove that the corresponding ODE doesn’t have any stable stationary points in [0,1]n, n is the number of variables, except the local maxima of the function to be optimized. Finally we show that this ODE and consequently the PBIL converge to one of these stable attractors.

A fuzzy clustering algorithm using cellular learning automata based evolutionary algorithm

In this paper, a new fuzzy clustering algorithm that uses cellular learning automata based evolutionary computing (CLA-EC) is proposed. The CLA-EC is a model obtained by combining the concepts of cellular learning automata and evolutionary algorithms. The CLA-EC is used to search for cluster centers in such a way that minimizes the clustering criterion. The simulation results indicate that the proposed algorithm produces clusters with acceptable quality with respect to clustering criterion and provides a performance that is superior to that of the C-means algorithm.

Fault Detection Structures for the Montgomery Multiplication over Binary Extension Fields

Finite field arithmetic is used in applications like cryptography, where it is crucial to detect the errors. Therefore, concurrent error detection is very beneficial to increase the reliability in such applications. Multiplication is one of the most important operations and is widely used in different applications. In this paper, we target concurrent error detection in the Montgomery multiplication over binary extension fields. We propose error detection schemes for two Montgomery multiplication architectures. First, we present a new concurrent error detection scheme using the time redundancy and apply it on semi-systolic array Montgomery multipliers. Then, we propose a parity based error detection scheme for the bit-serial Montgomery multiplier over binary extension Fields.