Fully Homomorphic Encryption over the Integers with Shorter Public Keys - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2011

Fully Homomorphic Encryption over the Integers with Shorter Public Keys

Résumé

At Eurocrypt 2010 van Dijk et al. described a fully homomorphic encryption scheme over the integers. The main appeal of this scheme (compared to Gentry’s) is its conceptual simplicity. This simplicity comes at the expense of a public key size in O~(λ10) which is too large for any practical system. In this paper we reduce the public key size to O~(λ7) by encrypting with a quadratic form in the public key elements, instead of a linear form. We prove that the scheme remains semantically secure, based on a stronger variant of the approximate-GCD problem, already considered by van Dijk et al. We also describe the first implementation of the resulting fully homomorphic scheme. Borrowing some optimizations from the recent Gentry-Halevi implementation of Gentry’s scheme, we obtain roughly the same level of efficiency. This shows that fully homomorphic encryption can be implemented using simple arithmetic operations.

Dates et versions

hal-01110216 , version 1 (27-01-2015)

Identifiants

Citer

Jean-Sébastien Coron, Avradip Mandal, David Naccache, Mehdi Tibouchi. Fully Homomorphic Encryption over the Integers with Shorter Public Keys. CRYPTO 2011 - 31st Annual Cryptology Conference, Aug 2011, Santa Barbara, CA, United States. pp.487-504, ⟨10.1007/978-3-642-22792-9_28⟩. ⟨hal-01110216⟩
394 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More