Big Data Analytics and Data Security in the Cloud via Fully Homomorphic Encryption

Authors: Victor Onomza Waziri, John K. Alhassan, Idris Ismaila, Moses Noel Dogonyaro

Abstract:

This paper describes the problem of building secure computational services for encrypted information in the Cloud Computing without decrypting the encrypted data; therefore, it meets the yearning of computational encryption algorithmic aspiration model that could enhance the security of big data for privacy, confidentiality, availability of the users. The cryptographic model applied for the computational process of the encrypted data is the Fully Homomorphic Encryption Scheme. We contribute a theoretical presentations in a high-level computational processes that are based on number theory and algebra that can easily be integrated and leveraged in the Cloud computing with detail theoretic mathematical concepts to the fully homomorphic encryption models. This contribution enhances the full implementation of big data analytics based cryptographic security algorithm.

Keywords: Data Analytics, Security, Privacy, Bootstrapping, and Fully Homomorphic Encryption Scheme.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1100060

References:

[1] Z. Brakerski, C. Gentry, And V. Vaikuntanathan,“(Leveled) Fully Homomorphic Encryption Without Bootstrapping,” In Itcs, 2012
[2] D. Boneh, E. J In Goh, And K. Nissim, “Evaluating 2-Dnf Formulas On Ciphertexts. In Theory Of Cryptography”; Conference, Tcc 2005, Volume 3378 of Lecture Notes in Computer Science, Pages, 325-341, Springer, 2005
[3] W. Diffie, M. E Hellman, “New Directions in Cryptography, IEEE Transactions on Information Theory, Volume IT-22, No. 6, (Online) http://ee.standford,edu/~hellman/publications/24.pdf
[4] C. Gentry; “A Fully Homomorphic Encryption Scheme” http://crypto.standford.edu/craig.thesis.pdf
[5] C. Gentry and S. Halevi, Implementing Gentry’s Fully Homomorphic Encryption Scheme, Preliminary Report, (Online). 2009 http://reasearcher,watson.ibm.com/researcher/files/usshail/fheimplementation. pdf
[6] C. Gentry, “Computing Arbitray Functions Data” Communication of the ACM, Vol. 53, pp 97-105, 2010
[7] S. Goldwasser and S. Micali: “Probabilistic Encryption & how to play mental porker keeping secret all partial information”, In proceedings of the 14th ACM symposium on the Theory of Computing (STOC ’82), New York, NY, USA, pp,21-53
[8] Goldwasser, S. and S. Micali, “ Probabilistic encryption”, In Journal of Computer and System Sciences, 1984, Vol 28, no. 2, pp270-299
[9] J. Katz & L. Yehud, “Introduction to Modern Cryptography”, Chapman& Hall/Crc Cryptography and Network Security, 2007.
[10] K. McCaney, “New Encryption method with promises end-to-end cloud security” http://gcn.com/Articles/2013/06/Encryption.end.to.end.cloud. security.aspx?Page =1
[11] J. Nittin, Saibal K. Pa and Dhananjay, K. Upadhyay; “Implementation and Analysis of Homomorphic Encryption Schemes, International Journal on
[12] P. Paillier: Public-key cryptosystems based on composite degree residuosity classes. In 18th Annual Eurocrypt Conference (EUROCRYPT’99), Prague, Czech Republic, Volume 1592,1999
[13] P. Meli and Timothy Grance, The NIST Definition of Cloud Computing, Special Publication, 2011 800-145, Recommendation of the National Institute of Standards and Technology.
[14] L. Ronald, Rivest, L. Addleman, and M. L. Dertouzos; ”On Data Banks and Privacy Homomorphism, Chapter on ata Banks and Privacy Homomorphisms, pages 169-180, academic press 1978
[15] S. Bajpai and P. Srivastava, “A Fully Encryption Implementation Cloud Computing, International Journal of Information and Computation Technology”, ISSN 09742239 Volume 4 (2014), pp. 811-816; copyright International Research Publications House. http://www.irphouse.com
[16] Y. Sophia, G. Vijay. S. Nabil, S. Emily, and Y. Arkady, “A Survey of CryptographyApproaches to Securing Big Data Analytics in the Cloud”, MIT Lincoln Laboratory, availalable (online), 2014: http://www.ieee.hpcc.org/2014/CD/index_htm_files/FinalPapers/28.pdf
[17] V. Dijk, M. Gentry, C. Halevi, V. Vaikuntanathan: “Fully Homomorphic Encryption over the Integers.” Advances in Cryptology- EUROCRYPT2010; 24-42
[18] V. Vaikunthanathan, “Computing Blindfolded: New Developments in Fully Homomorphic Encryption,” Supported by NSERC Discovery Grant and By DARPA under Agreement number FAS8750-11-1-0225. University of Toronto, 2013
[19] V. O. Waziri, J. K. Alhassan, O. Morufu and I. Ismaila, “Big Data Analytics and the Epitome of Fully Homomrphic Encryption Scheme for Cloud Computing Security”, International Journal of Developments in Big Data and Analytics Voolume 1 No.1, 2014, pp 19-40
[20] White Paper Big Data Analytics SAS www.sas.com/.../big-data-meetsbig- data-analytics-10577.pdf
[21] White Paper; An Oracle while Paper (March, “Advanced Analytics in Oracle Database” www.revolution-nalytics.com
[22] N. Rouda, Senior Analyst, White Paper, “Getting Real About Big Data: Build Versus Buy. Enterprise Strategy Group”, www.narius.com/esgbrief- on-big-data-analytics/esg-geetting-real-bigdata-2228170.pdf
[23] N. Rouda, Senior Analyst, “ESG White Paper, Getting Real About Big Data: Build Versus Buy. Enterprise Strategy Group”, www.narius.com/ esg-brief-on-big-data-analytics/esg-geetting-real-bigdata-2228170.pdf
[24] R.L. Rivest, A. Shamir, and L. Adleman, “A Method for Obtaining Digital Signatures and Public-Key Cryptosystems”, IEEE Trans. Inform. Theory, 1978
[25] T. El Gamal, “A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms”, IEEE Transactions On Information Theory, Vol. It-31, No. 4, July 1985
[26] C. E. Shannon and Warren Weaver, “The Mathematical Theory of Communication”, University of Illinois Press, 1949
[27] I. Damgard, M. Jurik and J. B. Nielsen, “A Generalization of Paillier's Public-Key System with Applications to Electronic Voting”, Aarhus University, Dept. of Computer Science, BRICS, 2001
[28] J. D. Cohen and M. J. Fischer, “A Robust and Verifiable Cryptographically Secure Election Scheme (Extended Abstract)”, YALEU/DCS/TR-416 July, 1985
[29] Z. Brakerski, C. Gentry, and V. Vaikuntanathan, “(Leveled) fully homomorphic, 2012