Efficient Fully Homomorphic Encryption from (Standard) LWE

By Zvika Brakerski, Vinod Vaikuntanathan. 2011

1,878 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Privacy & Security

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Citations in the corpus

HEAX: An Architecture for Computing on Encrypted Data (2019, background): “rk-many times (one per each RNS component). The result is accumulated in the BRAM banks. After k iterations, the second part of the computation – usually referred to as Modulus Switching(developed in [12]) – is performed. In Modulus Switching which executes Floor, the polynomial corresponding to the”
PIR with Compressed Queries and Amortized Query Processing (2018, methodology): “On the other hand, CPIR protocols [8, 21, 24, 27, 39, 45, 56, 57, 59, 60, 78] can be used with a database controlled by a single administrative domain (e.”
Crypto-Nets: Neural Networks over Encrypted Data (2014, background): “Even though there has been great progress in making FHE schemes more efﬁcient and secure (see, for example, Brakerski & Vaikuntanathan (2014)), this approach is currently not feasible for practical applications.”
On Deploying Secure Computing Commercially: Private Intersection-Sum Protocols and their Business Applications (2019, methodology): “The most efficient schemes of this type are based on the hardness of Ring-Learning-With-Errors [9, 8, 27, 23].”
Reusable garbled circuits and succinct functional encryption (2013, methodology): “When coupling our theorem with the ABE result of [30] and the FHE scheme of [12, 13], we obtain: C OROLLARY 1.2 (I NFORMAL ).”
Scale-Invariant Fully Homomorphic Encryption over the Integers (2014, methodology): “The ﬁrst generation of FHE schemes [Gen09, DGHV10, SV10, GH11, BV11a, BV11b] and [CMNT11, CNT12, CCK + 13] followed Gentry’s blueprint to achieve a fully homomorphic scheme.”
Accelerating Fully Homomorphic Encryption in Hardware (2015, background): “see [7], [8], [9], [10], we would like to take a snapshot of the attainable hardware performance of the GentryHalevi FHE variant.”
Lattice Signatures Without Trapdoors (2012, background): “This somewhat resembles the recent developments in constructions of fully-homomorphic encryption schemes, where the additional structure of ideal lattices was crucially used in earlier constructions [14, 15, 10], but was subsequently shown to be unnecessary [9, 2].”
Accelerating NTRU based homomorphic encryption using GPUs (2014, background): “Furthermore, during homomorphic circuit evaluation, due to modulus reduction [6], the modulus q (which determines the size of the polynomial coefficients) gradually shrinks.”
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.”
Faster Fully Homomorphic Encryption: Bootstrapping in Less Than 0.1 Seconds (2016, methodology): “Given a LWEs′ sample of a message μ ∈ T , the key switching procedure initially proposed in [7, 5] outputs a LWEs sample of the same μ without increasing the noise too much.”
How to Construct Quantum Random Functions (2012, background): “It also has numerous other applications throughout cryptography such as giving fully homomorphic encryption [16, 21], functional encryption [25], and certain types of program obfuscation [26, 42].”