Leveled Fully Homomorphic Encryption Schemes with Hensel Codes [article]

David William Honorio Araujo da Silva, Luke Harmon, Gaetan Delavignette, Carlos Paz de Araujo
2021 IACR Cryptology ePrint Archive  
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
more » ... ey 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.
dblp:journals/iacr/SilvaHDA21 fatcat:wyyv6mfgv5g6bc3tesw327vkpi