Abstract
With homomorphic encryption (HE), data can be processed in its encrypted form in the cloud computing (CC). This HE property can be considered as a useful solution to get over some concerns limiting the widespread adoption of CC services. Nevertheless, since CC environments are threatened by outsider and insider security attacks and since cloud consumers oftentimes access to CC services using resource-limited devices, the HE schemes need to be promoted in terms of security level and running time to work effectively. In El Makkaoui et al. (2016 international conference on big data and advanced wireless technologies, BDAW 2016, 2016b), we boosted the main Paillier’s scheme at security level by proposing a variant of the scheme called Cloud–Paillier. The proposed scheme addresses an exception of the Paillier’s scheme, supports the additive homomorphism over the integers and withstands more confidentiality attacks. For fast decryption, herein, we propose two fast variants of the Cloud–Paillier scheme. The proposed variants use moduli formed of \(k \ge 2\) distinct primes. The first variant utilizes the Chinese remainder theorem to decrypt. Whereas, the second variant sightly modifies the from of the Cloud–Paillier’s encryption algorithm and decrypts as in the Cloud–Paillier. Theoretical and simulation outcomes show that the suggested variants give a large decryption speed-up over the Cloud–Paillier while preserving a recommended security level.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Alam M, Emmanuel N, Khan T et al (2018) Garbled role-based access control in the cloud. J Ambient Intell Hum Comput 9:1153–1166. https://doi.org/10.1007/s12652-017-0573-6
Amoon M, El-Bahnasawy N, Sadi S et al (2018) On the design of reactive approach with flexible checkpoint interval to tolerate faults in cloud computing systems. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-018-1139-y
Armbrust M, Fox A, Griffith R et al (2009) Above the clouds: a Berkeley view of cloud computing. UC Berkeley Technical Report
Batut C, Belabas K, Bernardi D et al (2000) User’s Guide to PARI-GP. Université de Bordeaux I
Bhushan K, Gupta BB (2018) Distributed denial of service (DDoS) attack mitigation in software defined network (SDN)-based cloud computing environment. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-018-0800-9
Boneh D, Durfee G (2000) Cryptanalysis of RSA with private key d less than N/sup 0.292. IEEE Trans Inf Theory 46:1339–1349
Cai S, Gallina B, Nystrom D, Seceleanu C, Larsson A (2018) Tool-supported design of data aggregation processes in cloud monitoring systems. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-018-0730-6
Carmichael RD (1910) Note on a new number theory function. Bull Am Math Soc 16:232–238
Cheon JH et al (2013) Batch fully homomorphic encryption over the integers. In: Johansson T, Nguyen PQ (eds) Advances in cryptology—EUROCRYPT 2013. Lecture notes in computer science, vol 7881. Springer, Berlin, pp 315–335
El Makkaoui K, Beni-Hssane A, Ezzati A (2016) Cloud-ElGamal: an efficient homomorphic encryption scheme. In: 2016 international conference on wireless networks and mobile communications, WINCOM 2016, pp 63–66
El Makkaoui K, Beni-Hssane A, Ezzati A et al (2017) Fast cloud-RSA scheme for promoting data confidentiality in the cloud computing. Proced Comput Sci 113:33–40
El Makkaoui K, Beni-Hssane A, Ezzati A (2018) Speedy cloud-RSA homomorphic scheme for preserving data confidentiality in cloud computing. J Ambient Intell Human Comput. https://doi.org/10.1007/s12652-018-0844-x
El Makkaoui K, Ezzati A, Beni-Hssane A (2016) Securely adapt a paillier encryption scheme to protect the data confidentiality in the cloud environment. In: 2016 international conference on big data and advanced wireless technologies, BDAW 2016
El Makkaoui K, Ezzati A, Beni-Hssane A (2017) 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
El Makkaoui K, Ezzati A, Beni-Hssane A, Ouhmad S (2018) A swift Cloud–Paillier scheme to protect sensitive data confidentiality in cloud computing. Proced Comput Sci 134:83–90
ElGamal T (1985) A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Trans Inf Theory 31:469–472. https://doi.org/10.1109/TIT.1985.1057074
Gentry C (2009) Fully homomorphic encryption using ideal lattices. In: 41st annual ACM symposium on theory of computing, STOC’09, pp 169–178
Lenstra AK, Lenstra HW, Manasse MS et al (1993) The number field sieve. In: Lenstra AK, Lenstra HW (eds) The development of the number field sieve. Lecture notes in mathematics, vol 1554. Springer, Berlin, pp 11–42
Lenstra Jr HW (1987) Factoring integers with elliptic curves. Ann Math 126:649–673. https://doi.org/10.2307/1971363
Liu J, Ke L (2018) New efficient identity based encryption without pairings. J Ambient Intell Hum Comput. https://doi.org/10.1007/s12652-018-0756-9
Paillier P (1999) Public-key cryptosystems based on composite degree residuosity classes. In: Stern J (ed) Advances in cryptology—EUROCRYPT ’99. Lecture notes in computer science, vol 1592. Springer, Berlin, pp 223–238
Premkamal PK, Pasupuleti SK, Alphonse PJA (2018) A new verifiable outsourced ciphertext-policy attribute based encryption for big data privacy and access control in cloud. J Ambient Intell Hum Comput. https://doi.org/10.1007/s12652-018-0967-0
Rivest RL, Adleman L, Dertouzos ML (1978) On data banks and privacy homomorphisms. Found Secur Comput 4:169–180
Rivest RL, Shamir A, Adleman L (1978) A method for obtaining digital signatures and public-key cryptosystems. Commun ACM 21:120–126. https://doi.org/10.1145/359340.359342
Sun X, Zhang P, Sookhak M et al (2017) Utilizing fully homomorphic encryption to implement secure medical computation in smart cities. Pers Ubiquit Comput 21:831–839. https://doi.org/10.1007/s00779-017-1056-7
van Dijk M, Gentry C, Halevi S et al (2010) Fully homomorphic encryption over the integers. In: Gilbert H (ed) Advances in cryptology—EUROCRYPT 2010. Lecture notes in computer science, vol 6110. Springer, Berlin, pp 24–43
Wang X, Xu G, Wang M et al (2015) Mathematical foundations of public key cryptography. CRC Press, Boca Raton
Wei L, Zhu H, Cao Z et al (2014) Security and privacy for storage and computation in cloud computing. Inf Sci 258:371–386. https://doi.org/10.1016/j.ins.2013.04.028
Yi X, Paulet R, Bertino E (2014) Homomorphic encryption and applications. Springer, Heidelberg
Zhang M, Yao Y, Jiang Y et al (2018) Accountable mobile E-commerce scheme in intelligent cloud system transactions. J Ambient Intell Hum Comput 9:1889–1899. https://doi.org/10.1007/s12652-017-0672-4
Acknowledgements
We would like to thank professor Chafik Boufrioua for the proofreading of the paper and the anonymous reviewers for their precious comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
El Makkaoui, K., Ezzati, A., Beni-Hssane, A. et al. Fast Cloud–Paillier homomorphic schemes for protecting confidentiality of sensitive data in cloud computing. J Ambient Intell Human Comput 11, 2205–2214 (2020). https://doi.org/10.1007/s12652-019-01366-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12652-019-01366-3