CASTAGNOS, Guilhem; LAGUILLAUMIE, Fabien

doi:10.1007/978-3-319-16715-2_26

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CASTAGNOS, Guilhem
Lithe and fast algorithmic number theory [LFANT]
Institut de Mathématiques de Bordeaux [IMB]

LAGUILLAUMIE, Fabien
Arithmetic and Computing [ARIC]

Langue

Communication dans un congrès

Ce document a été publié dans

Lecture Notes in Computer Science, Lecture Notes in Computer Science, The Cryptographer's Track at the RSA Conference 2015, 2015-04-20, San Francisco. n° 9048

Résumé en anglais

We design a linearly homomorphic encryption scheme whose security relies on the hardness of the decisional Diffie-Hellman problem. Our approach requires some special features of the underlying group. In particular, its order is unknown and it contains a subgroup in which the discrete logarithm problem is tractable. Therefore, our instantiation holds in the class group of a non maximal order of an imaginary quadratic field. Its algebraic structure makes it possible to obtain such a linearly homomorphic scheme whose message space is the whole set of integers modulo a prime p and which supports an unbounded number of additions modulo p from the ciphertexts. A notable difference with previous works is that, for the first time, the security does not depend on the hardness of the factorization of integers. As a consequence, under some conditions, the prime p can be scaled to fit the application needs.< Réduire

Mots clés en anglais

Linearly Homomorphic Encryption

Orders of Quadratic Fields

Diffie-Hellman Assumptions

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194298

DOI

http://dx.doi.org/10.1007/978-3-319-16715-2_26

Projet Européen

Lattices: algorithms and cryptography

Project ANR

Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251