Speedy Cloud-RSA homomorphic scheme for preserving data confidentiality in cloud computing

Homomorphic encryption (HE) technique provides a third party with the ability to execute operations on ciphertexts. This property can be considered as a good solution to overcome some barriers limiting the widespread adoption of cloud services. However, since cloud environments are more threatened by security attacks and since cloud consumers often access to cloud services using resource-constrained devices, the HE schemes have to be promoted at security level and at running time to work efficiently. In El Makkaoui et al. (Cloud-RSA: an enhanced homomorphic encryption scheme. In: Rocha A, Serrhini M, Felgueiras C (eds) Europe and MENA cooperation advances in information and communication technologies. Advances in intelligent systems and computing, vol 520. Springer, Cham, pp 471–480, 2017b), we boosted RSA scheme at security level, Cloud-RSA. In this paper, we suggest two variants of Cloud-RSA scheme in order to speed up its decryption process. The variants are based on modifying the form of Cloud-RSA modulus and exponents. The first variant uses a modulus formed of two or more distinct primes and employs the Chinese remainder theorem (CRT) to encrypt and decrypt. Whereas, the second variant uses a modulus of the form n=prqs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n=p^rq^s$$\end{document} for r≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r\ge 2$$\end{document} and s≥1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s \ge 1$$\end{document}, and applies the Hensel lifting and the CRT to decrypt. Theoretical and simulation results show that the proposed variants provide a large decryption speedup over Cloud-RSA.