On Ideal Lattices and Learning with Errors over Rings

By Vadim Lyubashevsky, Chris Peikert, Oded Regev. 2010

2,898 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

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Citations in the corpus

Honeycrisp: large-scale differentially private aggregation without a trusted core (2019, methodology): “Ring-LWE: Honeycrisp requires an additively homomorphic cryptosystem to aggregate user inputs, and we instantiate our scheme using the simple “two-element” Ring-LWE-based encryption scheme of [54].”
XPIR : Private Information Retrieval for Everyone (2016, methodology): “As the pre and post-processing is public and reversible, security is directly based on the ring learning with errors problem (Ring-LWE) [22], as for the unmodiﬁed scheme in [28].”
Multiparty Computation from Somewhat Homomorphic Encryption (2012, background): “In [22] the authors specialise the decomposition (3) (by selecting appropriate rows and columns) in the case m′ = m1 and k = r, to show that to show that, upto a permutation of the rows, the matrix CRTm is equal to ( Iφ(r) ⊗ DFTm1 ) · T ∗ m,m1 · (CRTr ⊗ Im1) where Tm,m1 ∗ is another diagonal matrix ”
A Survey on Homomorphic Encryption Schemes (2017, background): “suggested another significant improvement on the LWE problem that may lead to new applications by introducing the ring-LWE (RLWE) problem (Lyubashevsky et al. 2013).”
Private genome analysis through homomorphic encryption (2015, methodology): “The security of this scheme is based on the (decisional) Ring Learning With Errors (RLWE) assumption, which was first introduced by Lyu-bashevsky, Peikert and Regev [23].”
An FPGA co-processor implementation of Homomorphic Encryption (2014, methodology): “Specifically, our contribution to the Proceed program has been the development of FPGA based hardware primitives to accelerate the computation on encrypted data using an FHE cryptosystem based on NTRU-like lattice techniques [3] with additional with additional support for efficient key switching and”
Homomorphic Encryption (2017, background): “Perhaps the most significant improvement comes from working over large extension rings rather than over the integers, relying on the ring-LWE hardness assumption (RLWE) [69].”
Efficient and Privacy-Enhanced Federated Learning for Industrial Artificial Intelligence (2020, methodology): “To implement our protocol efﬁciently, we utilize the Ring-LWE introduced by Lyubashevsky et al. [32].”
Somewhat Practical Fully Homomorphic Encryption (2012, methodology): “In this section we recall a very simple and elegant encryption scheme based on the RLWE problem introduced by Lyubashevsky, Peikert and Regev [15].”
HEPCloud: An FPGA-Based Multicore Processor for FV Somewhat Homomorphic Function Evaluation (2018, background): “Following [24] one may sample the key and the error polynomials from a common distribution x.”
Homomorphic Evaluation of the AES Circuit (2012, methodology): “Following [16,11], the specific norm that we use to evaluate the magnitude of the”
Pseudorandom Functions and Lattices (2012, methodology): “For a prime modulus q = 1 mod 2n and the error distribution χ described above, the decision-RLWE problem is as hard as the search problem, via a reduction that runs in time q · poly(n) [25].”