The functionality of classically-instructed remotely prepared random secret qubits was introduced in (Cojocaru et al 2018) as a way to enable classical parties to participate in secure quantum computation and communications protocols. The idea is that a classical party (client) instructs a quantum party (server) to generate a qubit to the server's side that is random, unknown to the server but known to the client. Such task is only possible under computational assumptions. In this contribution we define a simpler (basic) primitive consisting of only BB84 states, and give a protocol that realizes this primitive and that is secure against the strongest possible adversary (an arbitrarily deviating malicious server). The specific functions used, were constructed based on known trapdoor one-way functions, resulting to the security of our basic primitive being reduced to the hardness of the Learning With Errors problem. We then give a number of extensions, building on this basic module: extension to larger set of states (that includes non-Clifford states); proper consideration of the abort case; and verifiablity on the module level. The latter is based on "blind self-testing", a notion we introduced, proved in a limited setting and conjectured its validity for the most general case.
Classical client remote state preparation (CC − RSP) is a primitive where a fully classical party (client) can instruct the preparation of a sequence of random quantum states on some distant party (server) in a way that the description is known to the client but remains hidden from the server. This primitive has many applications, most prominently, it makes blind quantum computing possible for classical clients. In this work, we give a protocol for classical client remote state preparation, that requires minimal resources. The protocol is proven secure against honest-but-curious servers and any malicious third party in a game-based security framework. We provide an instantiation of a trapdoor (approximately) 2-regular family of functions whose security is based on the hardness of the Learning-With-Errors problem, including a first analysis of the set of usable parameters. We also run an experimentation on IBM’s quantum cloud using a toy function. This is the first proof-of-principle experiment of classical client remote state preparation.
Secure delegated quantum computing allows a computationally weak client to outsource an arbitrary quantum computation to an untrusted quantum server in a privacy-preserving manner. One of the promising candidates to achieve classical delegation of quantum computation is classical-client remote state preparation (RSP CC ), where a client remotely prepares a quantum state using a classical channel. However, the privacy loss incurred by employing RSP CC as a sub-module is unclear. In this work, we investigate this question using the Constructive Cryptography framework by Maurer and Renner [MR11]. We first identify the goal of RSP CC as the construction of ideal RSP resources from classical channels and then reveal the security limitations of using RSP CC . First, we uncover a fundamental relationship between constructing ideal RSP resources (from classical channels) and the task of cloning quantum states. Any classically constructed ideal RSP resource must leak to the server the full classical description (possibly in an encoded form) of the generated quantum state, even if we target computational security only. As a consequence, we find that the realization of common RSP resources, without weakening their guarantees drastically, is impossible due to the no-cloning theorem. Second, the above result does not rule out that a specific RSP CC protocol can replace the quantum channel at least in some contexts, such as the Universal Blind Quantum Computing (UBQC) protocol of Broadbent et al. [BFK09]. However, we show that the resulting UBQC protocol cannot maintain its proven composable security as soon as RSP CC is used as a subroutine. Third, we show that replacing the quantum channel of the above UBQC protocol by the RSP CC protocol QFactory of Cojocaru et al. [CCKW19] preserves the weaker, game-based, security of UBQC.
A proof of work (PoW) is an important cryptographic construct enabling a party to convince others that they invested some effort in solving a computational task. Arguably, its main impact has been in the setting of cryptocurrencies such as Bitcoin and its underlying blockchain protocol, which received significant attention in recent years due to its potential for various applications as well as for solving fundamental distributed computing questions in novel threat models. PoWs enable the linking of blocks in the blockchain data structure and thus the problem of interest is the feasibility of obtaining a sequence (chain) of such proofs. In this work, we examine the hardness of finding such chain of PoWs against quantum strategies. We prove that the chain of PoWs problem reduces to a problem we call multi-solution Bernoulli search, for which we establish its quantum query complexity. Effectively, this is an extension of a threshold direct product theorem to an average-case unstructured search problem. Our proof, adding to active recent efforts, simplifies and generalizes the recording technique of Zhandry (Crypto'19). As an application, we revisit the formal treatment of security of the core of the Bitcoin consensus protocol, the Bitcoin backbone (Eurocrypt'15), against quantum adversaries, while honest parties are classical and show that protocol's security holds under a quantum analogue of the classical “honest majority'' assumption. Our analysis indicates that the security of Bitcoin backbone is guaranteed provided the number of adversarial quantum queries is bounded so that each quantum query is worth O(p−1/2) classical ones, where p is the success probability of a single classical query to the protocol's underlying hash function. Somewhat surprisingly, the wait time for safe settlement in the case of quantum adversaries matches the safe settlement time in the classical case.
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