Certain investigations on Point multiplication algorithm in Elliptic curve over finite field for Parallel computations

Abstract

Elliptic Curve Cryptosystem is one of Asymmetric Key newlineCryptosystems which provides a high security for wireless and wired newlineApplications It is implemented with the help of polynomial number theory newlineand finite field Here a finite field has two important operations known as newlinepoint addition and point multiplication Normally In these operations the newlinetime complexity of the point multiplication is higher than the time complexity newlineof point addition So it is necessary to find out suitable implementation for newlinepoint multiplication to take minimum amount of clock cycles to reduce newlinepower consumption and to support the software scheduling for parallel newlineprocessing For these purpose the finite field is defined in two cases They newlineare prime field and binary field Besides Elliptic Curve is implemented newlinebased on this finite field in two ways such as Elliptic Curve over prime field newlinefor software applications and Elliptic Curve over binary field for hardware newlineapplications Based on this The Elliptic Curve over finite field is combined newlinewith Cryptography or Digital Signature and it is proposed with four different newlinetypes of algorithms Here the proposed methodologies are implemented with newlinehelp of code scheduling to support parallel processing through divide and newlineconquer methodology They have been implemented experimented and newlinetested successfully which are briefly noted as follows newline