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.
Secure computation in the presence of tamper-proof hardware tokens is proven under the assumption that the holder of the token is only given black-box access to the functionality of the token. Starting with the work of Goldreich and Ostrovsky [GO96], a long series of works studied tamper-proof hardware for realizing two-party functionalities in a variety of settings. In this work we focus our attention on two important complexity measures of stateless token-based secure computation: round complexity and hardness assumptions and present the following results in the two-party setting: • A round optimal generic secure protocol in the plain model assuming one-way functions, where the tokens are created by a single party. • A round optimal generic UC secure protocol assuming one-way functions. Our constructions are proven in the real/ideal paradigm with security in the presence of static malicious adversaries. As a side contribution, we identify a flaw in one of the feasibility results regarding UC secure protocols in the tamper proof model proved in the work of Goyal, Ishai, Sahai, Venkatesan and Wadia (TCC 2010) and correct history by attributing the work of Choi, Katz, Schroöder, Yerukhimovic and Zhou (TCC 2014) to establishing the (same) feasibility result.
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.