Fully Homomorphic Encryption with Polylog Overhead

By Craig Gentry, Shai Halevi, Nigel P. Smart. 2012

566 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

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Citations in the corpus

PIR with Compressed Queries and Amortized Query Processing (2018, methodology): “We implement this operation in SEAL by porting the Galois group actions algorithm from Gentry et al. [44, §4.2].”
Gazelle: A Low Latency Framework for Secure Neural Network Inference (2018, methodology): “This abstraction can be instantiated with essentially all modern lattice-based homomorphic encryption schemes, e.g., [4], [6], [13], [15].”
Multiparty Computation from Somewhat Homomorphic Encryption (2012, methodology): “In recent independent work [24, 2, 16], Meyers at al.”
Homomorphic Evaluation of the AES Circuit (2012, methodology): “In Section 2 we review the main features of BGV-type cryptosystems [4,3], and briefly survey the techniques for homomorphic computation on packed ciphertexts from SV and GHS [20,11].”
Practical Covertly Secure MPC for Dishonest Majority - Or: Breaking the SPDZ Limits (2013, background): “This is only sketched, the reader is referred to [6, 15, 16] for more details; our goal is to present enough detail to explain the key generation protocol later.”
FHEW: Bootstrapping Homomorphic Encryption in Less Than a Second (2015, background): “Improving the eﬃciency of Gentry’s scheme has received even more attention [23,6,21,20,19,18,17,2,1], resulting in enhanced asymptotic performance, and some reference implementations and libraries [23,17] that are eﬃcient enough to be run on a personal computer.”
Efficient, Oblivious Data Structures for MPC (2014, methodology): “It has been used previously in cryptography for twoparty oblivious shuffling [17], and also in fully homomorphic encryption [13] and private function evaluation [23].”
A Fast Single Server Private Information Retrieval Protocol with Low Communication Cost (2014, methodology): “We describe it here with improvements introduced in [33, 20, 34].”
(Leveled) Fully Homomorphic Encryption without Bootstrapping (2014, unknown): “TRADING OFF DEGREE FOR DIMENSION IN GLWE In this section, we present a new technique, termed ring switching in follow-up work [Gentry et al. 2012a], which allows trading off the parameters d and n of the GLWE problem.”
CryptoNets: Applying Neural Networks to Encrypted Data with High Throughput and Accuracy (2016, methodology): “Another application of the CRT allows us to perform Single Instruction Multiple Data (SIMD) operations at no extra cost Gentry et al. (2012b).”
Accelerating Somewhat Homomorphic Evaluation using FPGAs (2015, background): “More specifically, lattice-based [22, 21, 32], integer-based [15, 10, 11] and learning-with-errors (LWE) or (ring) learning with errors ((R)LWE) based encryption [6, 23, 24] schemes were introduced in just a few years.”
Bandwidth Efficient PIR from NTRU (2014, methodology): “Batching was introduced by Smart and Vercauteren [8, 9].”
Algorithms in HElib (2014, methodology): “Gentry, Halevi, and Smart showed [10] how to use the SV “ciphertext packing” technique to perform asymptotically efficient computation, where a (wide enough) T -gate arithmetic circuit can be evaluated homomorphically in time T · polylog(k), with k the security parameter.”
Compressible FHE with Applications to PIR (2019, background): “In fact, not just the rate but the overhead of an entire FHE computation can be reduced, sometimes to just a polylogarithmic function of the security parameter [GHS12].”