Cryptology ePrint Archive: Report 2017/548
Fully Homomorphic Encryption from the Finite Field Isomorphism Problem
Yarkın Doröz and Jeffrey Hoffstein and Jill Pipher and Joseph H. Silverman and Berk Sunar and 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.
Category / Keywords: public-key cryptography / Finite field isomorphism, fully homomorphic encryption, lattice-based cyrptopgraphy
Date: received 6 Jun 2017
Contact author: ydoroz at wpi edu
Available format(s): PDF | BibTeX Citation
Version: 20170608:194050 (All versions of this report)
Short URL: ia.cr/2017/548
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