Candidate Multilinear Maps from Ideal Lattices

By Sanjam Garg, Craig Gentry, Shai Halevi. 2013

756 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Geometry and Topology

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Citations in the corpus

Obfuscator-LLVM -- Software Protection for the Masses (2015, background): “One usually refers to such an adversary as a whitebox adversary [45].”
Multiparty Key Exchange, Efficient Traitor Tracing, and More from Indistinguishability Obfuscation (2014, methodology): “The first such protocols [11,21,36] are based on multilinear maps.”
Lattice Signatures and Bimodal Gaussians (2013, background): “In addition, researchers are rapidly discovering new lattice-based primitives, such as fully-homomorphic encryption [10], multi-linear maps [9], and attribute-based encryption [14], that had no previous constructions based on classical numbertheoretic techniques.”
Fairness in an Unfair World: Fair Multiparty Computation from Public Bulletin Boards (2017, background): “Since present constructions [26, 27, 36, 38] of multilinear maps are quite inefficient, we view our first construction as a feasibility result.”
Scalable Zero Knowledge Via Cycles of Elliptic Curves (2014, background): “Alternative zk-SNARKs constructions What are the advantages or disadvantages of pairing-based zk-SNARKs inwhich the pairing is not instantiatedvia a pairing-friendly elliptic curve, but insteadvia lattice techniques [51]?Moreover, are there preprocessing zk-SNARKs that are not based on pairings? (E.”
Post-Quantum Key Exchange for the TLS Protocol from the Ring Learning with Errors Problem (2015, neutral): “While lattice-based primitives [1], [2] have been used to achieve exciting new cryptographic functionalities like fully homomorphic encryption [3] and multilinear maps [4], there has also been a great deal of work on instantiating traditional cryptographic functionalities using lattices.”
GGHLite: More Efficient Multilinear Maps from Ideal Lattices (2014, methodology): “In 2013, Garg, Gentry and Halevi [9] introduced the ﬁrst “approximate” multilinear maps contruc-tion, based on ideal lattices, and the powerful notion of graded encoding scheme .”
On the existence of extractable one-way functions (2014, background): “They show that, under algebraic assumptions closely related to multilinear maps [26, 20], their construction satisfies the relaxed notion of indistinguishability obfuscation (IO) [2], for which no impossibility results are known.”