M-ary Precomputation-Based Accelerated Scalar Multiplication Algorithms for Enhanced Elliptic Curve Cryptography

TL;DR

This paper introduces an M-ary precomputation-based scalar multiplication algorithm for elliptic curve cryptography that significantly improves efficiency and reduces memory usage, validated through experiments and simulations.

Contribution

It presents a novel M-ary precomputation method that optimizes scalar multiplication in ECC, reducing computational complexity and memory requirements.

Findings

Up to 59% reduction in encryption time on secp256k1

30% memory savings in cryptographic operations

Reduces communication and simulation times in network scenarios

Abstract

Efficient scalar multiplication is critical for enhancing the performance of elliptic curve cryptography (ECC), especially in applications requiring large-scale or real-time cryptographic operations. This paper proposes an M-ary precomputation-based scalar multiplication algorithm, aiming to optimize both computational efficiency and memory usage. The method reduces the time complexity from $\Theta(Q \log p)$ to $\Theta\left(\frac{Q \log p}{\log Q}\right)$ and achieves a memory complexity of $\Theta\left(\frac{Q \log p}{\log^2 Q}\right)$. Experiments on ElGamal encryption and NS3-based communication simulations validate its effectiveness. On secp256k1, the proposed method achieves up to a 59\% reduction in encryption time and 30\% memory savings. In network simulations, the binary-optimized variant reduces communication time by 22.1\% on secp384r1 and simulation time by 25.4\% on secp521r1. The results demonstrate the scalability, efficiency, and practical applicability of the proposed algorithm. The source code will be publicly released upon acceptance.