Elliptic Curve Cryptography on Constrained Devices: A Comparative Study of Point Multiplication Methods

Constrained-resource devices struggle with implementing strong encryption due to limited capabilities. Elliptic Curve Cryptography (ECC) is a promising solution offering enhanced security with smaller key sizes. However, microcontrollers face challenges in executing ECC efficiently, particularly in point multiplication processes crucial for encryption. This study aims to compare various methods of multiplying points on elliptic curves in different coordinate systems, analyze the efficiency and performance of these methods, and explain the logical reasons for preferring the Montgomery ladder point multiplication method in the projective coordinate system for devices with limited resources. The research uses Python programming language to implement these methods on the secp256k1 curve.