# Fully Homomorphic Encryption Scheme for Securing Cloud Data

## DOI:

https://doi.org/10.21928/uhdjst.v7n2y2023.pp40-49## Keywords:

Cryptography, Cloud, Data security, Data privacy, Information security## Abstract

One of the pioneer and important fields in the computer science area is cloud computing. The data within cloud computing are usually transformed to it from local storage; therefore, the security of this data is an important issue. To solve this data security issue, it is important that cloud service providers (CSPs) store encrypted versions of user data. Before transmitting data to the cloud provider, it was encrypted using traditional encryption schemes. Nevertheless, for these schemes, the private key must be provided to the server to be used for the decryption on the other side before any calculations, yielding a security risk and issue for the cloud data. Homomorphic encryption provides a capable solution to this issue since it enables calculations on encrypted data with no need to be decrypted and the private encryption key is not compromised. A new fully homomorphic encryption scheme to protect cloud data is proposed in this paper, it is called NAZUZ. The NAZUZ scheme is based on prime modular operations and encrypts messages by operating on each character without converting them to binary. NAZUZ security relies on the difficulty of factoring large integer numbers and introduces noise complexity to the plaintext through the number of CSP users.

## References

B. Alabdullah, N. Beloff and M. White. “Rise of Big Data-Issues and Challenges”. Society National Computer Conference (NCC), Saudi Arabia, 2018.

D. Gonzales, J. M. Kaplan, E. Saltzman, Z. Winkelman and D. Woods. “Cloud-trust-a security assessment model for infrastructure as a service (IaaS) clouds”. IIEEE Transactions on Cloud Computing, vol. 5, no. 3, pp. 523-536, 2017.

R. Hamza, A. Hassan, A. Ali, M. Bashir, S. Al Qhutani, T. Tawfeeg and A. Yousif. “Towards secure big data analysis via fully homomorphic encryption algorithms”. Entropy, vol. 24, no. 4, p. 519, 2022.

B. Vankudoth and D. Vasumathi. “Homomorphic encryption techniques for securing data in cloud computing: A survey”. International Journal of Computer Applications, vol. 160, no. 6, pp. 1-5, 2017.

K. Sangani. “Sony security laid bare”. Engineering and Technology, vol. 6, no. 8, pp. 74-77, 2011.

R. L. Rivest, L. Adleman and M. L. Dertouzos. “On data banks and privacy homomorphisms. In: Foundations of Secure Computation”. Academic Press, New York, 1978, pp. 169-180.

M. Alia. “Combining public-key encryption with digital signature scheme. In: Advances in Intelligent Systems and Computing”. Springer, Germany, 2016, pp. 870-878.

A. C. Yao. “Protocols for Secure Computations. Proceedings of the 23rd Annual Symposium on Foundations of Computer Science (SFCS ‘82)”. IEEE Computer Society, 1982, pp. 160-164.

S. Goldwasser and S. Micali. “Probabilistic encryption”. Journal of Computer and System Sciences, vol. 28, no. 2, pp. 270-299, 1984.

T. Elgamal. “A public key cryptosystem and a signature scheme based on discrete logarithms”. IEEE Transactions on Information Theory, vol. 31, no. 4, pp. 469-472, 1985.

P. Paillier. “Public-key cryptosystems based on composite degree residuosity classes. In: Advances in Cryptology-Eurocrypt ’99”. vol. 1592, Springer, Germany, 1999, pp. 223-238.

C. Gentry. “Fully Homomorphic Encryption Using Ideal Lattices. In: Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing (STOC ‘09)”, 2009, pp. 169-178.

M. Dijk, C. Gentry, S. Halevi and V. Vaikuntanathan. “Fully homomorphic encryption over the integers. In: Advances in Cryptology-Eurocrypt”. Springer, Germany, vol. 6110, pp. 24-43, 2010.

N. Smart and F. Vercauteren. “Fully homomorphic encryption with relatively small key and ciphertext sizes. In: Public Key Cryptography-PKC”. 2010, Springer, Germany 2010, pp. 420-443.

J. H. Cheon, H. Choe, D. Lee and Y. Son. “Faster linear transformations in HElib, revisited”. IEEE Access, vol. 7, pp. 50595- 50604, 2019.

L. Xiao, O. Bastani and I. L. Yen. “An Efficient Homorphic Encryption Protocol for Multi-User Systems”. IACR Cryptology, Bellevue, WA, 2012.

T. Maha and E. L. H. Said. “Secure cloud computing through homomorphic encryption”. Computing Research Repository, vol. 1409, 2014.

A. Reem and E. Khaled. “Cloud Computing Algebra Homomorphic Encryption Scheme Based on Fermat’s Little Theorem”. The American Society of Engineering Education, United States, 2013.

R. Hayward and C. Chiangb. “Parallelizing fully homomorphic encryption for a cloud environment”. Journal of Applied Research and Technology, vol. 13, no. 2, pp. 245-252, 2015.

A. Frederik, C. Boyd, C. Carr, K. Gjøsteen, A. J¨aschke, C. A. Reuter and M. Strand. “A Guide to Fully Homomorphic Encryption”. vol. 1192. IACR Cryptology, Bellevue, WA, 2015.

S. S. Hamad and A. M. Sagheer. “Design of fully homomorphic encryption by prime modular operation”. Telfor Journal, vol. 10, no. 2, pp. 118-122, 2018.

F. Xiao, J. Wang, M. Wei, C. Liu, V. Le and J. Xu. “Privacy Data Protection Scheme of Industrial Field Equipment Based on Fully Homomorphic Encryption. In: 2023 International Conference on Information Networking (ICOIN)”. Bangkok, Thailand, 2023, pp. 236-241.

S. Hashim and M. Benaissa. “Fully Homomorphic Encryption Accelerator Using DSP Embedded Multiplier. In: 2023 15th International Conference on Computer Research and Development (ICCRD)”. Hangzhou, China, 2023, pp. 278-284.

B. H. M. Tan, H. T. Lee, H. Wang, S. Ren and K. M. M. Aung. “Efficient private comparison queries over encrypted databases using fully homomorphic encryption with finite fields”. IEEE Transactions on Dependable and Secure Computing, vol. 18, no. 6, pp. 2861-2874, 2021.

B. Dan, G. Eu-Jin and N. Kobbi. “Evaluating 2-DNF formulas on ciphertexts. In: Proceedings of Theory of Cryptography Conference”. vol. 3378, 2005, pp. 325-341.

M. Fellows and N. Koblitz. “Combinatorial Cryptosystems Galore!. In: Second International Conference on Finite Fields: Theory, Applications, and Algorithms August (Contemporary Mathematics) of Finite Fields: Theory, Applications, and Algorithms, vol. 168, 1993, pp. 51-61

G. Craig. “A Fully Homomorphic Encryption Scheme. Ph.D. Dissertation”. Stanford University, 2009.

L. Cardoso dos Santos, G. Rodrigues Bilar and F. Dacêncio Pereira. “Implementation of the fully homomorphic encryption scheme over integers with shorter keys”. In: 2015 7th International Conference on New Technologies, Mobility and Security (NTMS), Paris, 2015, pp. 1-5.

R. Oded. “On Lattices, Learning with Errors, Random Linear Codes, and Cryptography. In: Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing (STOC ‘05)”, 2005, pp. 84-93.

H. Jeffrey, P. Jill and J. S. Joseph. “NTRU: A Ring-Based Public Key Cryptosystem. In: International Algorithmic Number Theory Symposium”. Springer, Germany. pp. 267-288, 1998.

G. Craig. “Computing arbitrary functions of encrypted data”. Communications of the ACM, vol. 53, no. 3, pp. 97-105, 2010.

J. Li, D. Song, S. Chen and X. Lu. “A Simple Fully Homomorphic Encryption Scheme Available in Cloud Computing. In: 2012 IEEE 2nd International Conference on Cloud Computing and Intelligence Systems”. Hangzhou, 2012, pp. 214-217.

A. Acar, H. Aksu, A. S. Uluagac and M. Conti. “A survey on homomorphic encryption schemes: Theory and implementation”. ACM Computing Surveys. vol. 51, no. 4, pp. 1-35, 2018.

## Downloads

## Published

## How to Cite

*UHD Journal of Science and Technology*,

*7*(2), 40–49. https://doi.org/10.21928/uhdjst.v7n2y2023.pp40-49

## Issue

## Section

## License

Copyright (c) 2023 Tara Al Attar, Mohammed Anwar MOHAMMED

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.