Fully Homomorphic Encryption from the Finite Field Isomorphism Problem

Yarkın Doröz; Jeffrey Hoffstein; Jill Pipher; Joseph H.  Silverman; Berk Sunar; William Whyte; Zhenfei Zhang

Paper 2017/548

Fully Homomorphic Encryption from the Finite Field Isomorphism Problem

Yarkın Doröz, Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman, Berk Sunar, William Whyte, and Zhenfei Zhang

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. MINOR revision.
Keywords: Finite field isomorphism fully homomorphic encryption lattice-based cyrptopgraphy
Contact author(s): ydoroz @ wpi edu
History: 2017-06-08: received
Short URL: https://ia.cr/2017/548
License: CC BY

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}
}