On Perfectly Secure 2PC in the OT-hybrid model.

Bar Alon, Anat Paskin-Cherniavsky

Bar Alon, Anat Paskin-Cherniavsky

Vladimir Kolesnikov, Payman Mohassel, Ben Riva +1 more

Payman Mohassel, Mike Rosulek

Carmit Hazay, Muthuramakrishnan Venkitasubramaniam

Ishai, Kushilevitz, Ostrovsky and Sahai (STOC 2007, SIAM JoC 2009) introduced the powerful “MPC-in-the-head” technique that provided a general transformation of information-theoretic MPC protocols secure against passive adversaries to a ZK proof in a “black-box” way. In this work, we extend this technique and provide a generic transformation of any semi-honest secure two-party computation (2PC) protocol (with mild adaptive security guarantees) in the so called oblivious-transfer hybrid model to an adaptive ZK proof for any NP-language, in a “black-box” way assuming only one-way functions. Our basic construction based on Goldreich-Micali-Wigderson’s 2PC protocol yields an adaptive ZK proof with communication complexity proportional to quadratic in the size of the circuit implementing the NP relation. Previously such proofs relied on an expensive Karp reduction of the NP language to Graph Hamiltonicity (Lindell and Zarosim (TCC 2009, Journal of Cryptology 2011)). We also improve our basic construction to obtain the first linear-rate adaptive ZK proofs by relying on efficient maliciously secure 2PC protocols. Core to this construction is a new way of transforming 2PC protocols to efficient (adaptively secure) instance-dependent commitment schemes. As our second contribution, we provide a general transformation to construct a randomized encoding of a function f from any 2PC protocol that securely computes a related functionality (in a black-box way). We show that if the 2PC protocol has mild adaptive security guarantees then the resulting randomized encoding (RE) can be decomposed to an offline/online encoding. As an application of our techniques, we show how to improve the construction of Lapidot and Shamir (Crypto 1990) to obtain “input-delayed” ZK proofs which are proofs where the honest prover’s algorithm does not require the actual statement until the last round. An interesting corollary we obtain using these proofs are first constructions of a 4-round non-malleable commitments scheme based on oneway permutations where the underlying one-way permutation is used in a black-box way. Previous constructions either required more number of rounds or made non-black-box usage of the underlying primitives.

Nico Döttling, Satrajit Ghosh, Jesper Buus Nielsen +2 more

We introduce a new approach to actively secure two-party computation based on so-called oblivious linear function evaluation (OLE), a natural generalisation of oblivious transfer (OT) and a special case of the notion of oblivious polynomial evaluation introduced by Naor and Pinkas at STOC 1999. OLE works over a finite field F. In an OLE the sender inputs two field elements a ƒ F and b ƒ F, and the receiver inputs a field element x ∈ F and learns only ƒx) = ax + b. Our protocol can evaluate an arithmetic circuit over a finite field F given black-box access to OLE for F. The protocol is unconditionally secure and consumes only a constant number of OLEs per multiplication gate. An OLE over a field F of size O(2κ) be implemented with communication O(κ). This gives a protocol with communication complexity O(C κ) for large enough fields, where C is an arithmetic circuit computing the desired function. This asymptotically matches the best previous protocols, but our protocol at the same time obtains significantly smaller constants hidden by the big-O notation, yielding a highly practical protocol. Conceptually our techniques lift the techniques for basing practical actively secure 2PC of Boolean circuits on OT introduced under the name TinyOT by Nielsen, Nordholt, Orlandi and Burra at Crypto 2012 to the arithmetic setting. In doing so we develop several novel techniques for generating various flavours of OLE and combining these. We believe that the efficiency of our protocols, both in asymptotic and practical terms, establishes OLE and its variants as an important foundation for efficient actively secure 2PC.