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Vincent ZUCCA
État académique
Thèse en cours...
Sujet: Implementation de fonctions cryptographiques homomorphiques et d'outils de cryptanalyse
Direction de thèse:
Ellipse bleue: doctorant, ellipse jaune: docteur, rectangle vert: permanent, rectangle jaune: HDR. Trait vert: encadrant de thèse, trait bleu: directeur de thèse, pointillé: jury d'évaluation à mi-parcours ou jury de thèse.
Productions scientifiques
A Full RNS Variant of FV like Somewhat Homomorphic Encryption Schemes
International audience
Since Gentry's breakthrough work in 2009, homomorphic cryptography has received a widespread attention. Implementation of a fully homomorphic cryptographic scheme is however still highly expensive. Somewhat Homomorphic Encryption (SHE) schemes, on the other hand, allow only a limited number of arithmetical operations in the encrypted domain, but are more practical. Many SHE schemes have been proposed, among which the most competitive ones rely on (Ring-) Learning With Error (RLWE) and operations occur on high-degree polynomials with large coecients. This work focuses in particular on the Chinese Remainder Theorem representation (a.k.a. Residue Number Systems) applied to large coecients. In SHE schemes like that of Fan and Vercauteren (FV), such a representation remains hardly compatible with procedures involving coecient-wise division and rounding required in decryption and homomorphic multiplication. This paper suggests a way to entirely eliminate the need for multi-precision arithmetic, and presents techniques to enable a full RNS implementation of FV-like schemes. For dimensions between 2 11 and 2 15 , we report speed-ups from 5⇥ to 20⇥ for decryption, and from 2⇥ to 4⇥ for multiplication.
Selected Areas in Cryptography - SAC LNCS Selected Areas in Cryptography - SAC http://hal.upmc.fr/hal-01371941 Selected Areas in Cryptography - SAC, Aug 2016, St. John's, Newfoundland and Labrador, Canada. Selected Areas in Cryptography - SAC LNCS, <https://www.engr.mun.ca/~sac2016/organization/program/> https://www.engr.mun.ca/~sac2016/organization/program/ARRAY(0x7f4f388dce98) 2016-08-09
Prover efficient public verification of dense or sparse/structured matrix-vector multiplication
International audience
With the emergence of cloud computing services, computationally weak devices (Clients) can delegate expensive tasks to more powerful entities (Servers). This raises the question of verifying a result at a lower cost than that of recomputing it. This verification can be private, between the Client and the Server, or public, when the result can be verified by any third party. We here present protocols for the verification of matrix-vector multiplications, that are secure against malicious Servers. The obtained algorithms are essentially optimal in the amortized model: the overhead for the Server is limited to a very small constant factor, even in the sparse or structured matrix case; and the computational time for the public Verifier is linear in the dimension. Our protocols combine probabilistic checks and cryptographic operations, but minimize the latter to preserve practical efficiency. Therefore our protocols are overall more than two orders of magnitude faster than existing ones.
ACISP 2017 - 22nd Australasian Conference on Information Security and Privacy https://hal.archives-ouvertes.fr/hal-01503870 ACISP 2017 - 22nd Australasian Conference on Information Security and Privacy, Jul 2017, Auckland, New Zealand. Springer, 10343, pp.115-134, 2017, Lecture Notes in Computer Science. <http://acisp.massey.ac.nz/>. <10.1007/978-3-319-59870-3_7> http://acisp.massey.ac.nz/ARRAY(0x7f4f3888bb28) 2017-07-03
Efficient reductions in cyclotomic rings - Application to Ring-LWE based FHE schemes
International audience
With Fully Homomorphic Encryption (FHE), it is possible to process encrypted data without access to the private-key. This has a wide range of applications, most notably the offloading of sensitive data processing. Most research on FHE has focused on the improvement of its efficiency, namely by introducing of schemes based on Ring-Learning With Errors (RLWE), and techniques such as batching, which allows for the encryption of multiple messages in the same ciphertext. Much of the related research has focused on RLWE relying on power-of-two cy-clotomic polynomials. While it is possible to achieve efficient arithmetic with such polynomials, one cannot exploit batching. Herein, the efficiency of ring arithmetic underpinned by non-power-of-two cyclomotic polyno-mials is analyzed and improved. Two methods for polynomial reduction are proposed, one based on the Barrett reduction and the other on a Montgomery representation. Speed-ups of up to 2.66 are obtained for the reduction operation using an i7-5960X processor when compared with a straightforward implementation of the Barrett reduction. Moreover, the proposed methods are exploited to enhance homomorphic multiplication of Fan-Vercauteren (FV) and Brakerski-Gentry-Vaikuntantahan (BGV) encryption schemes, producing experimental speed-ups of up to 1.37.
Selected Areas of Cryptography 2017 http://hal.upmc.fr/hal-01585516 Selected Areas of Cryptography 2017, Aug 2017, Ottawa, CanadaARRAY(0x7f4f3888bca8) 2017-08-16