[Resource Topic] 2021/1281: Leveled Fully Homomorphic Encryption Schemes with Hensel Codes

Welcome to the resource topic for 2021/1281

Title:
Leveled Fully Homomorphic Encryption Schemes with Hensel Codes

Authors: David W. H. A. da Silva, Luke Harmon, Gaetan Delavignette, Carlos Araujo

Abstract:

We propose the use of Hensel codes (a mathematical tool lifted from the theory of p-adic numbers) as an alternative way to construct fully homomorphic encryption (FHE) schemes that rely on the hardness of some instance of the approximate common divisor (AGCD) problem. We provide a self-contained introduction to Hensel codes which covers all the properties of interest for this work. Two constructions are presented: a private-key leveled FHE scheme and a public-key leveled FHE scheme. The public-key scheme is obtained via minor modifications to the private-key scheme in which we explore asymmetric properties of Hensel codes. The efficiency and security (under an AGCD variant) of the public-key scheme are discussed in detail. Our constructions take messages from large specialized subsets of the rational numbers that admit fractional numerical inputs and associated computations for virtually any real-world application. Further, our results can be seen as a natural unification of error-free computation (computation free of rounding errors over rational numbers) and homomorphic encryption. Experimental results indicate the scheme is practical for a large variety of applications.

ePrint: https://eprint.iacr.org/2021/1281

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .