Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages

By Zvika Brakerski, Vinod Vaikuntanathan. 2011

1,202 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Shai Halevi
2. Kim Laine
3. Wei Dai
4. Craig Gentry
5. Vinod Vaikuntanathan
6. Hao Chen
7. Miran Kim
8. Dan Boneh

In Computational Theory and Mathematics

1. Shai Halevi
2. Craig Gentry
3. Kim Laine
4. Chris Peikert
5. Hao Chen
6. Vinod Vaikuntanathan
7. Miran Kim
8. Michael Naehrig

Citations in the corpus

• PIR with Compressed Queries and Amortized Query Processing (2018, methodology): “XPIR [4] implements Stern’s CPIR protocol [70] using the BV lattice-based homomorphic cryptosystem [17].”
• XPIR : Private Information Retrieval for Everyone (2016, methodology): “This is basically the symmetric homomorphic encryption scheme of [28] with a composite modulus.”
• A Survey on Homomorphic Encryption Schemes (2017, methodology): “Af-terwards, another FHE scheme whose hardness based on Ring Learning with Error (RLWE) problems is suggested [Brakerski and Vaikuntanathan 2011].”
• Privacy-Preserving Classification on Deep Neural Network (2017, background): “These schemes have worse performances than the latter systems and so are no longer considered • Schemes based on learning with error (LWE) or ring learning with error (RLWE) problems such as Brakerski and Vaikuntanathans schemes [10], [11] and their famous optimization BrakerskiGentry-Vaikuntanathan”
• Fully Homomorphic Encryption with Polylog Overhead (2012, methodology): “Pick one such pair and merge the two arrays //Merge sparse arrays 7.”
• OpenFHE: Open-Source Fully Homomorphic Encryption Library (2022, positive): “Two switching methods are supported: the Brakerski-Vaikuntanathan [18] digit decomposition method and the Gentry-Halevi-Smart [35] “hybrid” method (adapted to the RNS design in [45]).”
• Scalable and Private Media Consumption with Popcorn (2016, methodology): “Examples of cryptosystems used in CPIR are the Paillier [79] and the lattice-based Ring-LWE [19] cryptosystems.”
• Labeled PSI from Fully Homomorphic Encryption with Malicious Security (2018, background): “Fully Homomorphic Encryption (FHE) is a form of encryption that allows arbitrary (Boolean or arithmetic) circuits to be evaluated directly on encrypted data without requiring access to the decryption key [49,24,9,10,7,22,8,26,17,13].”
• Simple Encrypted Arithmetic Library - SEAL v2.1 (2016, methodology): “The first such encryption scheme was invented by Craig Gentry in 2009 [21], and since then researchers have introduced a number of new and more efficient fully homomorphic encryption schemes [11, 10, 7, 9, 20, 30, 5, 23].”
• Candidate Indistinguishability Obfuscation and Functional Encryption for all Circuits (2013, background): “[22], [23], [24], [25], [26]), we show how to obtain an indistinguishability obfuscator for all polynomial-size circuits.”
• A Survey of Provably Secure Searchable Encryption (2014, neutral): “Chang and Mitzenmacher [2005] introduced a new simulation-based IND-CKA definition, which is a stronger version of IND1-CKA in the sense that an adversary cannot even distinguish indexes from two unequal size documents. This requires that unequal size documents have indexes that appear to contain th”
• Efficient Secure Matrix Multiplication Over LWE-Based Homomorphic Encryption (2016, methodology): “We use the SHE scheme proposed by B r a k e r s k i and V a i k u n t a n at h a n [3].”
• Reusable garbled circuits and succinct functional encryption (2013, background): “The big leap of the last decade towards computing over encrypted data has been fully homomorphic encryption (FHE) [11–14, 17, 20–22, 38, 51, 52].”
• (Leveled) Fully Homomorphic Encryption without Bootstrapping (2014, positive): “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. In particular, we show that these parameters can be traded off subject to the invariant that n · d remains constant. We not”
• Fully Homomorphic Encryption without Modulus Switching from Classical GapSVP (2012, background): “RLWE is a stronger assumption than LWE, but it can dramatically improve the efficiency of schemes [3, 4, 12].”