Evaluating 2-DNF Formulas on Ciphertexts

By Dan Boneh, Eu-Jin Goh, Kobbi Nissim. 2005

1,810 citations recorded by the source corpus.

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In Artificial Intelligence

Citations in the corpus

A Review of Homomorphic Encryption Libraries for Secure Computation (2018, background): “Some examples of Somewhat Homomorphic Encryption schemes are [4,5,6,7,8].”
A Survey on Homomorphic Encryption Schemes (2017, methodology): “This property of BGN is a signiﬁcant improvement to obtain an FHE scheme.”
Taking Proof-Based Verified Computation a Few Steps Closer to Practicality (2012, methodology): “For instance, the Boneh-Goh-Nissim homomorphic cryptosystem [19] can be adapted to evaluate circuits, Groth uses homomorphic commitments to produce a zero-knowledge argument protocol [33], and Applebaum et al.”
Simulation-Sound NIZK Proofs for a Practical Language and Constant Size Group Signatures (2006, background): “Recently Groth, Ostrovsky and Sahai [30] have constructed NIZK proofs from composite order bilinear groups introduced by Boneh, Goh and Nissim [11].”
Cryptanalysis of a homomorphic encryption scheme from ISIT 2008 (2012, methodology): “After the introduction of privacy homomorphism, many schemes have been proposed, such as additive homomorphic encryption schemes [16], [1], [23], [30], [24], [9], [15], [18], [20], [25] and multiplicative homomorphic encryption schemes [10].”
Privacy-Preserving Machine Learning for Speech Processing (2012, background): “We briefly overview the Paillier [Paillier, 1999b] and BGN [Boneh et al., 2005] cryptosystems below.”
Privacy-Preserving Aggregation of Time-Series Data (2011, background): “g, El Gamal encryption and the BGN homomorphic encryption scheme [2].”
Structure-Preserving Signatures and Commitments to Group Elements (2010, background): “Homomorphic cryptosystems such as [ElG86, OU98, Pai99, BGN05 ] or Linear Encryption [BBS04] can be seen as homomorphic commitment schemes that are perfectly binding and computationally hiding.”
Privacy-Preserving ECG Classification With Branching Programs and Neural Networks (2011, methodology): “4) FullyHomomorphicEncryption: Asdescribedin[20],the interactiveapproach for multiplicationcurrentlyresults in faster SFE protocols than using schemes which also provide one (e.g., [ 37 ]) or arbitrarily many (e.g., [38]–[40]) multiplications under encryption, called fully homomorphic encryption.”
Fully Homomorphic Encryption from Ring-LWE and Security for Key Dependent Messages (2011, neutral): “, [21,12,30,6]).”
Bandwidth Efficient PIR from NTRU (2014, methodology): “Most of the single server cPIR schemes rely on costly algebraic operations with large operands such as modular multiplications [32, 2, 33], or pairing operations on elliptic curves [3] to realize the homomorphic evaluations.”
Efficient Privacy-Preserving Face Recognition (2009, neutral): “Further Protocol Improvements could be achieved with a different homomorphic encryption scheme that allows both, additions and multiplications [7,2,15] to avoid the additional communication round for computing Euclidean Distance.”
Securing Fog Computing for Internet of Things Applications: Challenges and Solutions (2018, methodology): “Currently, homomorphic encryption schemes, such as Paillier encryption [145] and BGN encryption [146], have been widely used in smart grid to achieve data aggregation.”
(Leveled) Fully Homomorphic Encryption without Bootstrapping (2014, neutral): “Prior to Gentry’s construction, there were already a few interesting homomorphic encryption schemes that could be called “somewhat homomorphic”, including that of Boneh et al. [2005] (that evaluates quadratic formulas using bilinear maps), Melchor et al.”
Generic Attacks on Secure Outsourced Databases (2016, methodology): “Broadly, the techniques include multi-party computation [47, 24], oblivious RAM [25, 25], searchable symmetric and structural encryp-1330 tion [45, 22, 13, 15, 14, 12, 40, 19, 33], functional encryption [9, 43], property-preserving encryption [5, 1, 7, 39] and homomorphic encryption [10, 21].”
Evaluating Branching Programs on Encrypted Data (2007, methodology): “Recently, an efﬁcient protocol for evaluating 2-DNF formulas and degree-2 polynomials on encrypted data was given by Boneh et al. [5].”