Paper 2015/047
Linearly Homomorphic Encryption from DDH
Guilhem Castagnos and Fabien Laguillaumie
Abstract
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.
Note: An extended abstract of this paper will be published in the proceedings of CT-RSA 2015. This is the full version.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Major revision. Proc. of CT-RSA 2015
- Keywords
- Linearly Homomorphic EncryptionOrders of Quadratic FieldsDiffie-Hellman Assumptions
- Contact author(s)
- guilhem castagnos @ math u-bordeaux1 fr
- History
- 2015-01-26: last of 2 revisions
- 2015-01-22: received
- See all versions
- Short URL
- https://ia.cr/2015/047
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2015/047,
author = {Guilhem Castagnos and Fabien Laguillaumie},
title = {Linearly Homomorphic Encryption from {DDH}},
howpublished = {Cryptology {ePrint} Archive, Paper 2015/047},
year = {2015},
url = {https://eprint.iacr.org/2015/047}
}
