Iterative sliding window method for shorter number of operations in modular exponentiation and scalar multiplication

Cryptography via public key cryptosystems (PKC) has been widely used for providing services such as confidentiality, authentication, integrity and non-repudiation. Other than security, computational efficiency is another major issue of concern. And for PKC, it is largely controlled by either modular exponentiation or scalar multiplication operations such that found in RSA and elliptic curve cryptosystem (ECC), respectively. One approach to address this operational problem is via concept of addition chain (AC), in which the exhaustive single operation involving large integer is reduced into a sequence of operations consisting of simple multiplications or additions. Existing techniques manipulate the representation of integer into binary and m-ary prior performing the series of operations. This paper proposes an iterative variant of sliding window method (SWM) form of m-ary family, for shorter sequence of multiplications *Corresponding author: Abdullah Muhammed, Faculty of Computer Science and Information Technology, Universiti Putra Malaysia, Serdang, 43400, Selangor, Malaysia E-mail: [email protected]