EC-Based Homomorphic Encryption and Bootstrapping using Koblitz Encoding

This paper introduces a novel approach to homomorphic encryption using elliptic curve cryptography with Koblitz encoding. We present a comprehensive framework for performing homomorphic operations on elliptic curves and address the critical challenge of noise management through an innovative bootstrapping technique. The proposed method leverages the algebraic structure of elliptic curves to encode messages as curve points, allowing computations directly on the encrypted data. Our key contribution is a bootstrapping mechanism that effectively resets accumulated noise, enabling sustained homomorphic evaluations. We provide rigorous mathematical proofs for correctness, security analysis under standard cryptographic assumptions, and performance benchmarks demonstrating the practical viability of our scheme for privacy-preserving computations in various application domains.