Fully Homomorphic Encryption over the Integers Revisited

Jung Hee Cheon; Damien Stehle

Paper 2016/837

Fully Homomorphic Encryption over the Integers Revisited

Jung Hee Cheon and Damien Stehle

Abstract

Two main computational problems serve as security foundations of current fully homomorphic encryption schemes: Regev's Learning With Errors problem (LWE) and Howgrave-Graham's Approximate Greatest Common Divisor problem (AGCD). Our first contribution is a reduction from LWE to AGCD. As a second contribution, we describe a new AGCD-based fully homomorphic encryption scheme, which outperforms all prior AGCD-based proposals: its security does not rely on the presumed hardness of the so-called Sparse Subset Sum problem, and the bit-length of a ciphertext is only softO(lambda), where lambda refers to the security parameter.

Note: Updated the Eurocrypt 2015 version, to fix a few minor errors.

Metadata

Available format(s): PDF
Publication info: A minor revision of an IACR publication in EUROCRYPT 2015
Contact author(s): damien stehle @ gmail com
History: 2016-09-04: revised; 2016-09-03: received; See all versions
Short URL: https://ia.cr/2016/837
License: CC BY

BibTeX

@misc{cryptoeprint:2016/837,
      author = {Jung Hee Cheon and Damien Stehle},
      title = {Fully Homomorphic Encryption over the Integers Revisited},
      howpublished = {Cryptology ePrint Archive, Paper 2016/837},
      year = {2016},
      note = {\url{https://eprint.iacr.org/2016/837}},
      url = {https://eprint.iacr.org/2016/837}
}