Threshold Garbled Circuits and Ad Hoc Secure Computation 📺
Garbled Circuits (GCs) represent fundamental and powerful tools in cryptography, and many variants of GCs have been considered since their introduction. An important property of the garbled circuits is that they can be evaluated securely if and only if exactly 1 key for each input wire is obtained: no less and no more. In this work we study the case when: 1) some of the wire-keys are missing, but we are still interested in computing the output of the garbled circuit and 2) the evaluator of the GC might have both keys for a constant number of wires. We start to study this question in terms of non-interactive multi-party computation (NIMPC) which is strongly connected with GCs. In this notion, there is a fixed number of parties (n) that can get correlated information from a trusted setup. Then these parties can send an encoding of their input to an evaluator, which can compute the output of the function. Similarly to the notion of ad hoc secure computation proposed by Beimel et al. [ITCS 2016], we consider the case when less than n parties participate in the online phase, and in addition we let these parties colluding with the evaluator. We refer to this notion as Threshold NIMPC. In addition, we show that when the number of parties participating in the online phase is a fixed threshold l <= n then it is possible to securely evaluate any l-input function. We build our result on top of a new secret-sharing scheme (which can be of independent interest) and on the results proposed by Benhamouda, Krawczyk and Rabin [Crypto 2017]. Our protocol can be used to compute any function in NC1 in the information-theoretic setting and any function in P assuming one-way functions. As a second (and main) contribution, we consider a slightly different notion of security in which the number of parties that can participate in the online phase is not specified, and can be any number c above the threshold l (in this case the evaluator cannot collude with the other parties). We solve an open question left open by Beimel, Ishai and Kushilevitz [Eurocrypt 2017] showing how to build a secure protocol for the case when c is constant, under the Learning with Errors assumption.
Multi-Client Functional Encryption for Separable Functions 📺
In this work, we provide a compiler that transforms a single-input functional encryption scheme for the class of polynomially bounded circuits into a multi-client functional encryption (MCFE) scheme for the class of separable functions. An $n$-input function $f$ is called separable if it can be described as a list of polynomially bounded circuits $f^1,..., f^n$ s.t. $f(x_1,..., x_n)= f^1(x_1)+ ... + f^n(x_n)$ for all $x_1,..., x_n$. Our compiler extends the works of Brakerski et al. [Eurocrypt 2016] and of Komargodski et al. [Eurocrypt 2017] in which a generic compiler is proposed to obtain multi-input functional encryption (MIFE) from single-input functional encryption. Our construction achieves the stronger notion of MCFE but for the less generic class of separable functions. Prior to our work, a long line of results has been proposed in the setting of MCFE for the inner-product functionality, which is a special case of a separable function. We also propose a modified version of the notion of decentralized MCFE introduced by Chotard et al. [Asiacrypt 2018] that we call outsourceable mulit-client functional encryption (OMCFE). Intuitively, the notion of OMCFE makes it possible to distribute the load of the decryption procedure among at most $n$ different entities, which will return decryption shares that can be combined (e.g., additively) thus obtaining the output of the computation. This notion is especially useful in the case of a very resource consuming decryption procedure, while the combine algorithm is non-time consuming. We also show how to extend the presented MCFE protocol to obtain an OMCFE scheme for the same functionality class.
Oblivious Transfer from Trapdoor Permutations in Minimal Rounds 📺
Oblivious transfer (OT) is a foundational primitive within cryptography owing to its connection with secure computation. One of the oldest constructions of oblivious transfer was from certified trapdoor permutations (TDPs). However several decades later, we do not know if a similar construction can be obtained from TDPs in general. In this work, we study the problem of constructing round optimal oblivious transfer from trapdoor permutations. In particular, we obtain the following new results (in the plain model) relying on TDPs in a black-box manner: – Three-round oblivious transfer protocol that guarantees indistinguishability-security against malicious senders (and semi-honest receivers). – Four-round oblivious transfer protocol secure against malicious adversaries with black-box simulation-based security. By combining our second result with an already known compiler we obtain the first round-optimal 2-party computation protocol that relies in a black-box way on TDPs. A key technical tool underlying our results is a new primitive we call dual witness encryption (DWE) that may be of independent interest.
Round Optimal Secure Multiparty Computation from Minimal Assumptions 📺
We construct a four round secure multiparty computation (MPC) protocol in the plain model that achieves security against any dishonest majority. The security of our protocol relies only on the existence of four round oblivious transfer. This culminates the long line of research on constructing round-efficient MPC from minimal assumptions (at least w.r.t. black-box simulation).