Paper 2017/548 Original: eprint.iacr.org/2017/548 ↗
Fully Homomorphic Encryption from the Finite Field Isomorphism Problem
Abstract
If $q$ is a prime and $n$ is a positive integer then any two finite fields of order $q^n$ are isomorphic. Elements of these fields can be thought of as polynomials with coefficients chosen modulo $q$, and a notion of length can be associated to these polynomials. A non-trivial isomorphism between the fields, in general, does not preserve this length, and a short element in one field will usually have an image in the other field with coefficients appearing to be randomly and uniformly distributed modulo $q$. This key feature allows us to create a new family of cryptographic constructions based on the difficulty of recovering a secret isomorphism between two finite fields. In this paper we describe a fully homomorphic encryption scheme based on this new hard problem.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2017-06-08: last updated
- 2017-06-08: published
- Short URL
- https://ia.cr/2017/548
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2017/548,
author = {Yarkın Doröz and Jeffrey Hoffstein and Jill Pipher and Joseph H. Silverman and Berk Sunar and William Whyte and Zhenfei Zhang},
title = {Fully Homomorphic Encryption from the Finite Field Isomorphism Problem},
howpublished = {Cryptology {ePrint} Archive, Paper 2017/548},
year = {2017},
url = {https://eprint.iacr.org/2017/548}
}