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Lecture notes in computer science

Distributed Protocols for Oblivious Transfer and Polynomial Evaluation

Aviad Ben Arie, Tamir Tassa

Published Jan 1, 2024• 1 citation
Publisher
DOI
10.1007/978-3-031-56235-8_4

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arXiv:2305.11114•May 18, 2023•0 citations
We describe efficient constructions for two oblivious twoparty computation problems: l-out-of-N Oblivious Transfer &d 'Oblivious Poly&nial Evaluation.The oblivious polynomial evaluation protocol is based on a new intractability assumption which is closely related to noisy polynomial re construction.A direct corollary of the l-out-of-N OT protccol is an efficient transformation of any Private Information Retrieval (PIR) protocol to a Symmetric PIR (SPIR) prc-tow1 without increasing the number of databases.The new construction for l-out-of-N OT is highly efficient -it requires only log N executions of a l-out-of-2 OT protocol.We also present a construction for k-out-of-N OT which is more efficient than k repetitions of l-out-of-N OT.The efficiency of the new OT protocols makes them useful for a variety of applications.These include oblivious sampling which can be used to securely compare the sizes of web search engines, protocols for privately solving the list intersection problem and for mutually authenticated key exchange based on (possibly weak) passwords, and protocols for anonymity preserving web usage metering.
Abstract—Oblivious polynomial evaluation is a protocol involving two parties, a sender whose input is a polynomial P, and a receiver whose input is a value x. At the end of the protocol, the receiver learns P (x) and nothing more about P, while the sender remains oblivious of both x and P (x). It is used as a primitive in many applications including protocols for private comparison of data, for mutually authenticated key exchange based on (possibly weak) passwords, and for anonymous coupons. In this paper, we describe a novel unconditionally secure oblivious polynomial evaluation protocol. Keywords—Multi-Party Computation, Oblivious Transfer, Oblivious Polynomial Evaluation.
XOR oblivious transfer is a universal cryptographic primitive that can be related to linear polynomial evaluation. We firstly introduce some bipartite quantum protocols for XOR oblivious transfer, which are not secure if one party cheats, and some of them can be combined with a classical XOR homomorphic encryption scheme for evaluation of linear polynomials modulo 2 with hybrid security. We then introduce a general protocol using modified versions of the XOR oblivious transfer protocols to evaluate linear polynomials modulo 2 with partial information-theoretic security. When combined with the ability to perform arbitrary quantum computation, this would lead to deterministic interactive two-party computation which is quite secure in the information-theoretic sense when the allowed set of inputs is large. For the task of classical function evaluation, although the quantum computation approach is still usable, we also discuss purely classical post-processing methods based on the proposed linear polynomial evaluation protocols.