Universally Composable Quantum Multi-Party Computation

The Universal Composability model (UC) by Canetti (FOCS 2001) allows for secure composition of arbitrary protocols. We present a quantum version of the UC model which enjoys the same compositionality guarantees. We prove that in this model statistically secure oblivious transfer protocols can be constructed from commitments. Furthermore, we show that every statistically classically UC secure protocol is also statistically quantum UC secure. Such implications are not known for other quantum security definitions. As a corollary, we get that quantum UC secure protocols for general multi-party computation can be constructed from commitments

Inductive dielectric analyzer

© 2017 IOP Publishing Ltd.One of the approaches to bypass the problem of electrode polarization in dielectric measurements is the free electrode method. The advantage of this technique is that, the probing electric field in the material is not supplied by contact electrodes, but rather by electromagnetic induction. We have designed an inductive dielectric analyzer based on a sensor comprising two concentric toroidal coils. In this work, we present an analytic derivation of the relationship between the impedance measured by the sensor and the complex dielectric permittivity of the sample. The obtained relationship was successfully employed to measure the dielectric permittivity and conductivity of various alcohols and aqueous salt solutions

Zero Knowledge Protocols from Succinct Constraint Detection

We study the problem of constructing proof systems that achieve both soundness and zero knowledge unconditionally (without relying on intractability assumptions). Known techniques for this goal are primarily *combinatorial*, despite the fact that constructions of interactive proofs (IPs) and probabilistically checkable proofs (PCPs) heavily rely on *algebraic* techniques to achieve their properties. We present simple and natural modifications of well-known algebraic IP and PCP protocols that achieve unconditional (perfect) zero knowledge in recently introduced models, overcoming limitations of known techniques. 1. We modify the PCP of Ben-Sasson and Sudan [BS08] to obtain zero knowledge for NEXP in the model of Interactive Oracle Proofs [BCS16,RRR16], where the verifier, in each round, receives a PCP from the prover. 2. We modify the IP of Lund, Fortnow, Karloff, and Nisan [LFKN92] to obtain zero knowledge for #P in the model of Interactive PCPs [KR08], where the verifier first receives a PCP from the prover and then interacts with him. The simulators in our zero knowledge protocols rely on solving a problem that lies at the intersection of coding theory, linear algebra, and computational complexity, which we call the *succinct constraint detection* problem, and consists of detecting dual constraints with polynomial support size for codes of exponential block length. Our two results rely on solutions to this problem for fundamental classes of linear codes: * An algorithm to detect constraints for Reed--Muller codes of exponential length. This algorithm exploits the Raz--Shpilka [RS05] deterministic polynomial identity testing algorithm, and shows, to our knowledge, a first connection of algebraic complexity theory with zero knowledge. * An algorithm to detect constraints for PCPs of Proximity of Reed--Solomon codes [BS08] of exponential degree. This algorithm exploits the recursive structure of the PCPs of Proximity to show that small-support constraints are locally spanned by a small number of small-support constraints

On the Exact Round Complexity of Secure Three-Party Computation

We settle the exact round complexity of three-party computation (3PC) in honest-majority setting, for a range of security notions such as selective abort, unanimous abort, fairness and guaranteed output delivery. Selective abort security, the weakest in the lot, allows the corrupt parties to selectively deprive some of the honest parties of the output. In the mildly stronger version of unanimous abort, either all or none of the honest parties receive the output. Fairness implies that the corrupted parties receive their output only if all honest parties receive output and lastly, the strongest notion of guaranteed output delivery implies that the corrupted parties cannot prevent honest parties from receiving their output. It is a folklore that the implication holds from the guaranteed output delivery to fairness to unanimous abort to selective abort. We focus on two network settings-- pairwise-private channels without and with a broadcast channel. In the minimal setting of pairwise-private channels, 3PC with selective abort is known to be feasible in just two rounds, while guaranteed output delivery is infeasible to achieve irrespective of the number of rounds. Settling the quest for exact round complexity of 3PC in this setting, we show that three rounds are necessary and sufficient for unanimous abort and fairness. Extending our study to the setting with an additional broadcast channel, we show that while unanimous abort is achievable in just two rounds, three rounds are necessary and sufficient for fairness and guaranteed output delivery. Our lower bound results extend for any number of parties in honest majority setting and imply tightness of several known constructions. The fundamental concept of garbled circuits underlies all our upper bounds. Concretely, our constructions involve transmitting and evaluating only constant number of garbled circuits. Assumption-wise, our constructions rely on injective (one-to-one) one-way functions

Efficient Fully Secure Computation via Distributed Zero-Knowledge Proofs

Secure computation protocols enable mutually distrusting parties to compute a function of their private inputs while revealing nothing but the output. Protocols with {\em full security} (also known as {\em guaranteed output delivery}) in particular protect against denial-of-service attacks, guaranteeing that honest parties receive a correct output. This feature can be realized in the presence of an honest majority, and significant research effort has gone toward attaining full security with good asymptotic and concrete efficiency. We present an efficient protocol for {\em any constant} number of parties $n$, with {\em full security} against $t<n/2$ corrupted parties, that makes a black-box use of a pseudorandom generator. Our protocol evaluates an arithmetic circuit $C$ over a finite ring $R$ (either a finite field or $R=\Z_{2^k}$) with communication complexity of $\frac{3t}{2t+1}S + o(S)$ $R$-elements per party, where $S$ is the number of multiplication gates in $C$ (namely, $<1.5$ elements per party per gate). This matches the best known protocols for the semi-honest model up to the sublinear additive term. For a small number of parties $n$, this improves over a recent protocol of Goyal {\em et al.} (Crypto 2020) by a constant factor for circuits over large fields, and by at least an $\Omega(\log n)$ factor for Boolean circuits or circuits over rings. Our protocol provides new methods for applying the sublinear-communication distributed zero-knowledge proofs of Boneh {\em et al.}~(Crypto 2019) for compiling semi-honest protocols into fully secure ones, in the more challenging case of $t>1$ corrupted parties. Our protocol relies on {\em replicated secret sharing} to minimize communication and simplify the mechanism for achieving full security. This results in computational cost that scales exponentially with $n$. Our main fully secure protocol builds on a new intermediate honest-majority protocol for verifying the correctness of multiplication triples by making a {\em general} use of distributed zero-knowledge proofs. While this intermediate protocol only achieves the weaker notion of {\em security with abort}, it applies to any linear secret-sharing scheme and provides a conceptually simpler, more general, and more efficient alternative to previous protocols from the literature. In particular, it can be combined with the Fiat-Shamir heuristic to simultaneously achieve logarithmic communication complexity and constant round complexity

On the Computational Overhead of MPC with Dishonest Majority

We consider the situation where a large number $n$ of players want to securely compute a large function $f$ with security against an adaptive, malicious adversary which might corrupt $t < cn$ of the parties for some given $c \in [0,1)$. In other words, only some arbitrarily small constant fraction of the parties are assumed to be honest. For any fixed $c$, we consider the asymptotic complexity as $n$ and the size of $f$ grows. We are in particular interested in the computational overhead, defined as the total computational complexity of all parties divided by the size of $f$. We show that it is possible to achieve poly-logarithmic computational overhead for all $c < 1$. Prior to our result it was only known how to get poly-logarithmic overhead for $c < \frac{1}{2}$. We therefore significantly extend the area where we can do secure multiparty computation with poly-logarithmic overhead. Since we allow that more than half the parties are corrupted, we can only get security with abort, i.e., the adversary might make the protocol abort before all parties learn their outputs. We can, however, for all $c$ make a protocol for which there exists $d > 0$ such that if at most $d n$ parties are actually corrupted in a given execution, then the protocol will not abort. Our result is solely of theoretical interest

Broadcast-Optimal Two-Round MPC

An intensive effort by the cryptographic community to minimize the round complexity of secure multi-party computation (MPC) has recently led to optimal two-round protocols from minimal assumptions. Most of the proposed solutions, however, make use of a broadcast channel in every round, and it is unclear if the broadcast channel can be replaced by standard point-to-point communication in a round-preserving manner, and if so, at what cost on the resulting security. In this work, we provide a complete characterization of the trade-off between number of broadcast rounds and achievable security level for two-round MPC tolerating arbitrarily many active corruptions. Specifically, we consider all possible combinations of broadcast and point-to-point rounds against the three standard levels of security for maliciously secure MPC protocols, namely, security with identifiable, unanimous, and selective abort. For each of these notions and each combination of broadcast and point-to-point rounds, we provide either a tight feasibility or an infeasibility result of two-round MPC. Our feasibility results hold assuming two-round OT in the CRS model, whereas our impossibility results hold given any correlated randomness

Guaranteed Output Delivery Comes Free in Honest Majority MPC

We study the communication complexity of unconditionally secure MPC with guaranteed output delivery over point-to-point channels for corruption threshold t < n/2, assuming the existence of a public broadcast channel. We ask the question: “is it possible to construct MPC in this setting s.t. the communication complexity per multiplication gate is linear in the number of parties?” While a number of works have focused on reducing the communication complexity in this setting, the answer to the above question has remained elusive until now. We also focus on the concrete communication complexity of evaluating each multiplication gate. We resolve the above question in the affirmative by providing an MPC with communication complexity O(Cn\phi) bits (ignoring fixed terms which are independent of the circuit) where \phi is the length of an element in the field, C is the size of the (arithmetic) circuit, n is the number of parties. This is the first construction where the asymptotic communication complexity matches the best-known semi-honest protocol. This represents a strict improvement over the previously best-known communication complexity of O(C(n\phi+\kappa)+D_Mn^2\kappa) bits, where \kappa is the security parameter and D_M is the multiplicative depth of the circuit. Furthermore, the concrete communication complexity per multiplication gate is 5.5 field elements per party in the best case and 7.5 field elements in the worst case when one or more corrupted parties have been identified. This also roughly matches the best-known semi-honest protocol, which requires 5.5 field elements per gate