Converting Pairing-Based Cryptosystems from Composite-Order Groups to Prime-Order Groups

By David Mandell Freeman. 2010

319 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Geometry and Topology, Information Systems

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Citations in the corpus

Secure Federated Submodel Learning (2019, background): “These basic settings make the secure aggregation protocol different from other relevant work about oblivious addition [19]–[21], or, more generally, secure multiparty computation [63]–[66], which requires direct peer-to-peer communication between clients; assumes the availability of multiple noncoll”
Predicate Encryption Supporting Disjunctions, Polynomial Equations, and Inner Products (2008, background): “(In follow-up work, Freeman [20] shows how to modify our construction so that it works using groups of prime order.”
Privacy and Access Control for Outsourced Personal Records (2015, methodology): “Therefore, we use a scheme transformation proposed by David Freeman [29], which works in prime-order groups and is more efﬁcient.”
Verifiable Delegation of Computation over Large Datasets (2011, background): “The subgroup membership assumption in composite order bilinear groups first appeared in [13], and has seen many recent applications in the areas of Identity Based Encryption (IBE), Hierarchical IBE, and others [25,13,8].”
Decentralizing Attribute-Based Encryption (2011, methodology): “We note that several systems such as BGN encryption [15], GrothOstrovsky-Sahai NIZK proofs [32], traitor tracing [16] , and predicate encryption [17, 36] were originally developed in the composite order setting, but later variants were developed in prime order groups [31, 48, 33, 35, 25, 26, 37].”
Charm: a framework for rapidly prototyping cryptosystems (2013, background): “Both David Freeman [44] and Alison Lewko [59] have recently proposed tools for this type of translation; however, all of these tools currently require human intervention.”
Practical constructions and new proof methods for large universe attribute-based encryption (2013, background): “In a recent result [22] building on [30, 32, 23, 17], one can actually “em-ulate” the eﬀects of the composite order groups by creating special subspaces of vectors, called dual vector spaces introduced by Okamoto and Takashima, and construct a large universe KP-ABE system on prime order groups.”
An Algebraic Framework for Diffie–Hellman Assumptions (2013, methodology): “This alternative formulation has conceptual advantages for some applications, for instance, it allowed to provide more instantiations of the original DDH-based scheme of Cramer and Shoup and it is also the most natural point of view for translating schemes originally constructed in composite order g”