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arXiv:1908.05584

Quantum preprocessing for security enhancement in classical two-party computation.

Li Zhi Yu

Published Aug 15, 2019• 0 citations
arXivHTMLPDF

Abstract

In classical two-party computation, a trusted initializer who prepares certain initial correlations, known as one-time tables, can help make the inputs of both parties information-theoretically secure. We propose some bipartite quantum protocols with possible aborts for approximately generating such bipartite classical correlations with varying degrees of privacy, without introducing a third party. Under some weak requirements for the parties, the security level is nontrivial for use in bipartite computation. We show that the security is sometimes dependent on the noise level, but we propose a method for dealing with noise. The security is forced security, which implies that the probability that some useful one-time tables are generated can approach $1$ in the noiseless case under quite weak assumptions about the parties, although the protocols allow aborts. We show how to use the generated one-time tables to achieve nontrivial information-theoretic security in generic two-party classical or quantum computation tasks, including (interactive) quantum homomorphic encryption. Our methods provide check-based implementations of some no-signaling correlations, including the PR-box type, with the help of communication which carry no information about the inputs in the generated correlations.

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In classical two-party computation, a trusted initializer who prepares certain initial correlations, known as one-time tables, can help make the inputs of both parties information-theoretically secure. We propose some bipartite quantum protocols with possible aborts for approximately generating such bipartite classical correlations with varying degrees of privacy, without introducing a third party. Under some weak requirements for the parties, the security level is nontrivial for use in bipartite computation. We show that the security is sometimes dependent on the noise level, but we propose a method for dealing with noise. The security is forced security, which implies that the probability that some useful one-time tables are generated can approach 111 in the noiseless case under quite weak assumptions about the parties, although the protocols allow aborts. We show how to use the generated one-time tables to achieve nontrivial information-theoretic security in generic two-party classical or quantum computation tasks, including (interactive) quantum homomorphic encryption. Our methods provide check-based implementations of some no-signaling correlations, including the PR-box type, with the help of communication which carry no information about the inputs in the generated correlations.
One-time tables are a class of two-party correlations that can help achieve information-theoretically secure two-party (interactive) classical or quantum computation. In this work we propose a bipartite quantum protocol for generating a simple type of one-time tables (the correlation in the Popescu-Rohrlich nonlocal box) with partial security. We then show that by running many instances of the first protocol and performing checks on some of them, asymptotically information-theoretically secure generation of one-time tables can be achieved. The first protocol is adapted from a protocol for semi-honest quantum oblivious transfer, with some changes so that no entangled state needs to be prepared, and the communication involves only one qutrit in each direction. We show that some information tradeoffs in the first protocol are similar to that in the semi-honest oblivious transfer protocol. We also obtain two types of inequalities about guessing probabilities in some protocols for generating one-time tables, from a single type of inequality about guessing probabilities in semi-honest quantum oblivious transfer protocols.
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.
Efficient models for secure computation often rely on offline preprocessed correlations, which subsequently enable private online computation from minimal assumptions. Within these models, the study of secure non-interactive reductions (SNIR) formalizes when one classical correlation can be non-interactively transformed into another, while guaranteeing information-theoretic simulation-based privacy. In this work, we introduce quantum secure non-interactive reductions (QSNIR), a natural extension of SNIR, in which the source and target resource are each a bipartite quantum state. Specifically, when the target resource is classical, our framework enables us to analyze the problem of disseminating private correlations from entanglement, in addition to classical resources. Our primary technical result is that QSNIR privacy in this context can be computed exactly via a semidefinite program (SDP) pair that quantifies an error operationally rooted in a simulation-based cheating advantage. We prove that QSNIR privacy is lower-bounded by a decision problem related to minimum-error state discrimination (MED), and use both definitions to compute exact one-shot privacy errors for universal two-party computation (2PC) preprocessing correlations.
A fundamental task in modern cryptography is the joint computation of a function which has two inputs, one from Alice and one from Bob, such that neither of the two can learn more about the other's input than what is implied by the value of the function. In this Letter, we show that any quantum protocol for the computation of a classical deterministic function that outputs the result to both parties (two-sided computation) and that is secure against a cheating Bob can be completely broken by a cheating Alice. Whereas it is known that quantum protocols for this task cannot be completely secure, our result implies that security for one party implies complete insecurity for the other. Our findings stand in stark contrast to recent protocols for weak coin tossing and highlight the limits of cryptography within quantum mechanics. We remark that our conclusions remain valid, even if security is only required to be approximate and if the function that is computed for Bob is different from that of Alice.
We consider the problem of securely generating useful instances of two-party correlations, such as many independent copies of a random oblivious transfer (OT) correlation, using a small amount of communication. This problem is motivated by the goal of secure computation with silent preprocessing, where a low-communication input-independent setup, followed by local ("silent") computation, enables a lightweight "non-cryptographic" online phase once the inputs are known. Recent works of Boyle et al. (CCS 2018, Crypto 2019) achieve this goal with good concrete efficiency for useful kinds of two-party correlations, including OT correlations, under different variants of the Learning Parity with Noise (LPN) assumption, and using a small number of "base'' oblivious transfers. The protocols of Boyle et al. have several limitations. First, they require a large number of communication rounds. Second, they are only secure against semi-honest parties. Finally, their concrete efficiency estimates are not backed by an actual implementation. In this work we address these limitations, making three main contributions: Eliminating interaction. Under the same assumption, we obtain the first concretely efficient 2-round protocols for generating useful correlations, including OT correlations, in the semi-honest security model. This implies the first efficient 2-round OT extension protocol of any kind and, more generally, protocols for non-interactive secure computation (NISC) that are concretely efficient and have the silent preprocessing feature. Malicious security. We provide security against malicious parties without additional interaction and with only a modest overhead; prior to our work, no similar protocols were known with any number of rounds. Implementation. Finally, we implemented, optimized, and benchmarked our 2-round OT extension protocol, demonstrating that it offers a more attractive alternative to the OT extension protocol of Ishai et al. (Crypto 2003) in many realistic settings.
Secure two-party computation considers the problem of two parties computing a joint function of their private inputs without revealing anything beyond the output. In this work, we consider the setting where the two parties (a classical Alice and a quantum Bob) can communicate only via a classical channel. Our first result shows that it is in general impossible to realize a two-party quantum functionality with black-box simulation in the case of malicious quantum adversaries. In particular, we show that the existence of a secure quantum computing protocol that relies only on classical channels would contradict the quantum no-cloning argument. We circumvent this impossibility following three different approaches. The first is by considering a weaker security notion called one-sided simulation security. This notion protects the input of one party (the quantum Bob) in the standard simulation-based sense and protects the privacy of the other party's input (the classical Alice). We show how to realize a protocol that satisfies this notion relying on the learning with errors assumption. The second way to circumvent the impossibility result, while at the same time providing standard simulation-based security also against a malicious Bob, is by assuming that the quantum input has an efficient classical representation. Finally, we focus our attention on the class of zero-knowledge functionalities and provide a compiler that takes as input a classical proof of quantum knowledge (PoQK) protocol for a QMA relation R and outputs a zero-knowledge PoQK for R that can be verified by classical parties. The direct implication of our result is that Mahadev's protocol for classical verification of quantum computations (FOCS'18) can be turned into a zero-knowledge proof of quantum knowledge with classical verifiers. To the best of our knowledge, we are the first to instantiate such a primitive.