Supervision : Jean-Claude BAJARD

Towards Efficient Arithmetic for Ring-LWE based Homomorphic Encryption

Fully homomorphic encryption is a kind of encryption offering the ability to manipulate encrypted data directly through their ciphertexts. In this way it is possible to process sensitive data without having to decrypt them beforehand, ensuring therefore the datas' confidentiality. At the numeric and cloud computing era this kind of encryption has the potential to considerably enhance privacy protection. However, because of its recent discovery by Gentry in 2009, we do not have enough hindsight about it yet. Therefore several uncertainties remain, in particular concerning its security and efficiency in practice, and should be clarified before an eventual widespread use.
This thesis deals with this issue and focus on performance enhancement of this kind of encryption in practice. In this perspective we have been interested in the optimization of the arithmetic used by these schemes, either the arithmetic underlying the Ring Learning With Errors problem on which the security of these schemes is based on, or the arithmetic specific to the computations required by the procedures of some of these schemes. We have also considered the optimization of the computations required by some specific applications of homomorphic encryption, and in particular for the classification of private data, and we propose methods and innovative technics in order to perform these computations efficiently. We illustrate the efficiency of our different methods through different software implementations and comparisons to the related art.

2016-2019 Publications

• 2019
  • J.‑C. Bajard, P. Martins, L. Sousa, V. Zucca : “Improving the Efficiency of SVM Classification with FHE”, IEEE Transactions on Information Forensics and Security, vol. 15, pp. 1709-1722, (Institute of Electrical and Electronics Engineers) (2019)
• 2018
  • V. Zucca : “Vers une arithétique efficace pour le chiffrement homomorphe basé sur le problème du Ring-LWE”, thesis, phd defence 06/25/2018, supervision Bajard, Jean-Claude (2018)
• 2017
  • J.‑C. Bajard, J. Eynard, A. Hasan, P. Martins, L. Sousa, V. Zucca : “Efficient reductions in cyclotomic rings - Application to Ring-LWE based FHE schemes”, Selected Areas of Cryptography 2017, Ottawa, Canada (2017)
  • J.‑G. Dumas, V. Zucca : “Prover efficient public verification of dense or sparse/structured matrix-vector multiplication”, ACISP 2017 - 22^nd Australasian Conference on Information Security and Privacy, vol. 10343, Lecture Notes in Computer Science, Auckland, New Zealand, pp. 115-134, (Springer) (2017)
• 2016
  • J.‑C. Bajard, J. Eynard, A. Hasan, V. Zucca : “A Full RNS Variant of FV like Somewhat Homomorphic Encryption Schemes”, Selected Areas in Cryptography - SAC LNCS, St. John's, Newfoundland and Labrador, Canada (2016)