In this paper we address the problem of protecting elliptic curve scalar multiplication
implementations against side-channel analysis by using the atomicity principle. First of all …

Double-base chains (DBCs) are widely used to speed up scalar multiplications on elliptic
curves. We present three results of DBCs. First, we display a structure of the set containing …

New formulae for point addition and point doubling on elliptic curves over prime fields are
presented. Based on these formulae, an improved Montgomery algorithm is proposed. The …

This paper introduces a novel implementation of the elliptic curve factoring method
specifically designed for medium-size integers such as those arising by billions in the …

This paper analyzes the Symbolic Ternary Form (STF) scalar multiplication algorithm and
binary scalar multiplication algorithm computation, compared with binary scalar …

The triple-base number system is used to speed up scalar multiplication. At present, the
main methods to calculate a triple-base chain are greedy algorithms. We propose a new …

We propose an algorithm to produce the optimal double-base chains (DBC) that minimize
the time used for computing a multi-scalar multiplication, one of bottleneck operations of …

Abstract The Elliptic Curve Method (ECM) is a versatile algorithm for determining prime
factors of medium-sized composite integers. It is commonly used in the sieving phase of the …

Abstract In Wireless Sensor Networks (WSNs), providing a robust security mechanism with
limited energy resources is very challenging because of sensor node's limited resources …

Triple-base number systems are mainly used in elliptic curve cryptography to speed up
scalar multiplication. We give an upper bound on the length of the canonical triple-base …