TITLE:
An Unbounded Fully Homomorphic Encryption Scheme Based on Ideal Lattices and Chinese Remainder Theorem
AUTHORS:
Zhiyong Zheng, Fengxia Liu, Kun Tian
KEYWORDS:
Fully Homomorphic Encryption, Ideal Lattices, Chinese Remainder Theorem, General Compact Knapsacks Problem
JOURNAL NAME:
Journal of Information Security,
Vol.14 No.4,
October
11,
2023
ABSTRACT: We propose an unbounded fully homomorphic encryption scheme, i.e. a scheme that allows one to compute
on encrypted data for any desired functions without needing to decrypt the data
or knowing the decryption keys. This is a rational solution to an old problem
proposed by Rivest, Adleman, and Dertouzos [1] in 1978, and to some new problems that appeared in Peikert [2] as open questions 10 and open questions 11 a few years ago. Our scheme is completely different from the
breakthrough work [3] of Gentry in 2009. Gentry’s bootstrapping technique constructs a fully homomorphic encryption (FHE) scheme from a somewhat homomorphic one that is powerful enough to
evaluate its own decryption function. To date, it remains the only known way of
obtaining unbounded FHE. Our construction of an unbounded FHE scheme is straightforward and can handle unbounded
homomorphic computation on any refreshed ciphertexts without bootstrapping
transformation technique.