The multiplier uses LUT’s as memory for their computations. The antisymmetric product coding (APC) and odd-multiple-storage (OMS) techniques were proposed for look-up-table (LUT) design. The APC and OMS techniques used for efficient memory-based multiplication. Therefore the combined approach provides a reduction in LUT size to onefourth of the conventional LUT. APC approach is combined with th...

SYNOPSIS Four patients with 'developmental dyscalculia' are described who were initially identified on the basis of clinical tests, reports of longstanding and severe difficulties in arithmetic, and psychological test results. Descriptive psychological testing indicated (1) that the arithmetical deficits could not be accounted for on the basis of a generally low level of intellectual functionin...

A new modular multiplication algorithm and its corresponding architecture is presented. It is optimised with respect to hardware complexity and latency. Based on the data flow of the well known interleaved modular multiplication the product of two n-bit-integers X and Y modulo M is computed by n iterations of a simple loop. The loop consists of one single carry save addition, a comparison of co...

In this paper, a round-table group optimization (RTGO) algorithm is presented. RTGO is a simple metaheuristic framework using the insights of research on group creativity. In a cooperative group, the agents work in iterative sessions to search innovative ideas in a common problem landscape. Each agent has one base idea stored in its individual memory, and one social idea fed by a round-table gr...

The most popular public-key cryptography systems nowadays are RSA and Elliptic Curve Cryptography (ECC). ECC is a type of public-key cryptosystem which uses the additive group of points on a nonsingular elliptic curve as a cryptographic medium. The basic operation in most elliptic curve cryptosystems is a scalar multiplication. Scalar Multiplication is the costliest operation among all in ECC w...

Let G be a semisimple Lie group, g its Lie algebra. For any symmetric space M over G we construct a new (deformed) multiplication in the space A of smooth functions on M. This multiplication is invariant under the action of the Drinfeld–Jimbo quantum group U h g and is commutative with respect to an involutive operator˜S : A⊗A → A⊗A. Such a multiplication is unique. Let M be a kählerian symmetr...

Digital filter construction method, which is optimal by parametric sensitivity, based on using of non-canonical hypercomplex number systems is proposed and investigated. It is shown that the use of non-canonical hypercomplex number system with greater number of non-zero structure constants in multiplication table can significantly improve the sensitivity of the digital filter.

In this paper, considering the concept of Universal Multiplication Table, we show that for every n ≥ 2, the inequality: M(n) = #{ij|1 ≤ i, j ≤ n} ≥ n2 N(n2) , holds true with: N(n) = n log 2 log log n ( 1+ 387 200 log log n ) . Then using this fact we show that the value c in the Linnik-Vinogradov’s result; M(n) = O (