Most practical public-key cryptosystems are based on modular exponentiation. A modular exponentiation is composed of repeated modular multiplications. Several methods have been proposed to reduce the execution time of a modular exponentiation, essentially aiming to reduce the execution time of each modular multiplication. The goal of this paper is to investigate three different integer multipli...

Multiplication is a basic operation in any signal processing application. Multiplication is the most important one among the four arithmetic operations like addition, subtraction, and division. Multipliers are usually hardware intensive, and the main parameters of concern are high speed, low cost, and less VLSI area. The propagation time and power consumption in the multiplier are always high. ...

It is well known that the gain–bandwidth product of an avalanche photodiode can be increased by utilizing a thin multiplication region. Previously, measurements of the excess noise factor of InP–InGaAsP–InGaAs avalanche photodiodes with separate absorption and multiplication regions indicated that this approach could also be employed to reduce the multiplication noise. This paper presents a sys...

A new and highly efficient architecture for elliptic curve scalar point multiplication is presented. To achieve the maximum architectural and timing improvements we have reorganized and reordered the critical path of the Lopez-Dahab scalar point multiplication architecture such that logic structures are implemented in parallel and operations in the critical path are diverted to noncritical path...

Digital signal processors (DSPs) are very important in various engineering disciplines. Fast multiplication is very important in DSPs for convolution, Fourier transforms, etc. A fast method for multiplication based on ancient Indian Vedic mathematics is proposed in this paper. The whole of Vedic mathematics is based on 16 sutras (word formulae) and manifests a unified structure of mathematics. ...

Abstract Efficiency in multiplication is very important in applications like signal processing, cryptosystems and coding theory. This paper presents the design of a fast multiplier using the Karatsuba algorithm to multiply two numbers using the technique of polynomial multiplication. The Karatsuba algorithm saves coefficient multiplications at the cost of extra additions as compared to the ordi...

PCLMULQDQ, a new instruction that supports GF(2)[x] multiplication, was introduced by Intel in 2010. This instruction brings dramatic change to software implementation of multiplication in GF(2m) fields. In this paper, we present improved Karatsuba formulae for multiplying two small binary polynomials, compare different strategies for PCLMULQDQbased multiplication in the five GF(2m) fields reco...

Bit is added to the left of the partial product using sign extension.products required to half that required by a simple add and shift method. A signed binary multiplication technique. Quarterly Journal of.Booths multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in twos complement notation. The above mentioned technique is inadequate when the multi...

The aim of this note is to generalize the Nakayama lemma to a class of multiplication modules over commutative rings with identity. In this note, by considering the notion of multiplication modules and the product of submodules of them, we state and prove two versions of Nakayama lemma for such modules. In the first version we give some equivalent conditions for faithful finitely generated mult...