Big number operation has always been a bottleneck to computer system as it imposes high
demand on computing power. With a limited power available, operations such as …

Elliptic curve based cryptosystem is an efficient public key cryptosystem, which is more
suitable for limited environments. The very expensive operation in elliptic curve based …

In the Elliptic Curve Cryptosystem, the multiplication of points is essential in the successful
computation of any operation. Reduction of time complexity for the mathematical operations …

We know the" signed-digit recoding algorithm" has less occurrence probability of the
nonzero digit than original binary number representation. The goal of study time-efficient …

This paper introduces CCS (complementary canonical sliding window) representation which
is an efficient class of the non-adjacent-form (NAF). The CCS representation is an extension …

The aim of Elliptic Curve Cryptosystems (ECC) is to achieve the same security level as RSA
but with shorter key size. The basic operation in the ECC is scalar multiplication which is an …

Modular multi-exponentiation [Formula: see text] is a very important but time-consuming
operation in many modern cryptosystems. In this paper, a fast modular multi-exponentiation …

Elliptic curve cryptosystems have been the focus of much attention as the benefits of elliptic
curve cryptography (ECC) become many such as a small software footprint, low hardware …

Efficient computation of the modular exponentiations is very important and useful for public-
key cryptosystems. In this paper, an efficient parallel binary exponentiation algorithm is …

Scalar multiplication is a very expensive operation in elliptic curve based cryptographic
protocol. In this paper, we propose a modified simultaneous elliptic curve scalar …