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.
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.
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.
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 of the computation. In this work, we take the first steps towards understanding the setting in which the two parties want to evaluate a joint quantum functionality while using only a classical channel between them. Our first result indicates that it is in general impossible to realize a two-party quantum functionality against malicious adversaries with black-box simulation, relying only on classical channels. The negative result stems from reducing the existence of a black-box simulator to an extractor for classical proof of quantum knowledge, which in turn leads to violation of the quantum no-cloning. Next, we introduce the notion of oblivious quantum function evaluation (OQFE). An OQFE is a two-party quantum cryptographic primitive with one fully classical party (Alice) whose input is (a classical description of a) quantum unitary, U, and a quantum party (Bob) whose input is a quantum state, ψ. In particular, Alice receives a classical output corresponding to the measurement of U(ψ) while Bob receives no output. In OQFE, Bob remains oblivious to Alice's input, while Alice learns nothing about ψ more than what can be learned from the output. We present two constructions, one secure against semi-honest parties and the other against malicious parties. Due to the no-go result mentioned above, we consider what is arguably the best possible notion obtainable in our model concerning malicious adversaries: one-sided simulation security. Our protocol relies on the assumption of injective homomorphic trapdoor OWFs, which in turn rely on the LWE problem. As a result, we put forward a first, simple and modular, construction of one-sided quantum two-party computation and quantum oblivious transfer over classical networks.
In cryptography, oblivious transfer (OT) is an important multi-party cryptographic primitive and protocol, that is suitable for many upper-layer applications, such as secure computation, remote coin-flipping, electrical contract signing and exchanging secrets simultaneously. However, some no-go theorems have been established, indicating that one-out-of-two quantum oblivious transfer (QOT) protocols with unconditional security are impossible. Fortunately, some one-out-of-two QOT protocols using the concept of Crépeau’s reduction have been demonstrated not to conform to Lo’s no-go theorem, but these protocols require more quantum resources to generate classical keys using all-or-nothing QOT to construct one-out-of-two QOT. This paper proposes a novel and efficient one-out-of-two QOT which uses quantum resources directly instead of wasting unnecessary resources to generate classical keys. The proposed protocol is not covered by Lo’s no-go theorem, and it is able to check the sender’s loyalty and avoid the attack from the receiver. Moreover, the entangled state of the proposed protocol is reusable, so it can provide more services for the participants when necessary. Compared with other QOT protocols, the proposed protocol is more secure, efficient, and flexible, which not only can prevent external and internal attacks, but also reduce the required resources and resource distribution time.
Oblivious transfer, a central functionality in modern cryptography, allows a party to send two one-bit messages to another who can choose one of them to read, remaining ignorant about the other, whereas the sender does not learn the receiver's choice. Oblivious transfer the security of which is information-theoretic for both parties is known impossible to achieve from scratch. The joint behavior of certain bi-partite quantum states is non-local, i.e., cannot be explained by shared classical information. In order to better understand such behavior, which is classically explainable only by communication, but does not allow for it, Popescu and Rohrlich have described a "non-locality machine": Two parties both input a bit, and both get a random output bit the XOR of which is the AND of the input bits. We show a close connection, in a cryptographic sense, between OT and the "PR primitive." More specifically, unconditional OT can be achieved from a single realization of PR, and vice versa. Our reductions, which are single-copy, information-theoretic, and perfect, also lead to a simple and optimal protocol allowing for inverting the direction of OT
Oblivious transfer is a fundamental cryptographic primitive that is useful for secure multiparty computation. There are several variants of oblivious transfer. We consider 1-out-of-2 oblivious transfer, where a sender sends two bits of information to a receiver. The receiver receives only one of the two bits, while the sender does not know which bit the receiver has received. Perfect quantum oblivious transfer with information-theoretic security is known to be impossible. We aim to find the lowest possible cheating probabilities. Bounds on cheating probabilities have been investigated for “complete” protocols, where if both parties follow the protocol, the bit value obtained by the receiver matches the sender's bit value. We instead investigate incomplete protocols, where the receiver obtains an incorrect bit value with probability p f . We present optimal noninteractive protocols where Alice's bit values are encoded in four symmetric pure quantum states, and where she cannot cheat better than with a random guess. We find the protocols such that for a given p f , Bob's cheating probability p r is as low as possible, and vice versa. Furthermore, we show that noninteractive quantum protocols can outperform noninteractive classical protocols and give a lower bound on Bob's cheating probability in interactive quantum protocols. Importantly for optical implementations, our protocols do not require entanglement nor quantum memory.