Additive Homomorphism for RSA via Exponentiation Encoding for IoT Security

Abstract

Homomorphic Encryption (HE) enables computation on encrypted data, an essential capability for preserving privacy in cloud computing and Internet of Things (IoT) environments. While Fully Homomorphic Encryption (FHE) supports arbitrary operations, its substantial computational overhead limits its use on resource-constrained devices. Partially Homomorphic Encryption (PHE) schemes like standard RSA are more efficient but are restricted to a single operation, such as multiplication.This paper introduces a novel method that extends the standard RSA cryptosystem to support secure addition on encrypted data. Our approach uses an exponentiation-based encoding technique that transforms the addition of plaintext values into a multiplicative operation on their ciphertexts. This design bypasses the complex, resource-intensive processing required by FHE, while preserving RSA’s inherent efficiency.We demonstrate the correctness and security of our scheme through implementation and evaluation. The results show that our method is highly efficient, providing a practical and lightweight solution for privacy-preserving computations in IoT and cloud-based applications. Specifically, our implementation achieves encryption in 0.04 ms, computation in 0.03 ms, and decryption in 0.4 ms, with a memory footprint of only 0.91 KB. At the same time, ciphertext expansion remains limited to the RSA modulus size, representing orders of magnitude efficiency gains compared to lightweight FHE schemes.