Elliptic Curve Point Multiplication Using Halving

Related Concepts

Elliptic Curve Cryptography; Square and Multiply Algorithm

Definition

Given a point Q on an elliptic curve, halving finds a point P so that Q = 2P. Halving can replace most doubles in point multiplication algorithms built on “double and add.”

Background

Elliptic curve cryptographic schemes require calculations of the type

$$kP = \underbrace{ P + \cdots + P }_{k}$$

where k is a large integer and the addition is over the elliptic curve (Elliptic Curves). The operation is known as scalar or point multiplication, and dominates the execution time of signature and encryption schemes based on elliptic curves. Double-and-add variations of familiar square-and-multiply methods (Square and Multiply Algorithm) for modular exponentiation are commonly used to find kP. Windowing methods can significantly reduce the number of point additions required, but the number of point doubles remains essentially unchanged.

Among techniques to reduce the cost of the point doubles in point...