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Quantum Science and Technology

Asymmetric secure multi-party quantum computation with weak clients against dishonest majority

Theodoros Kapourniotis, Elham Kashefi, Dominik Leichtle, Luka Music, Harold Ollivier

Published Jan 28, 2025• 13 citations
Publisher

Abstract

Abstract Secure multi-party computation (SMPC) protocols allow several parties distrusting each other to collectively compute a function on their inputs, without revealing the input values. In this paper, we introduce a protocol that lifts SMPC to its quantum counterpart—secure multi-party quantum computation (SMPQC) for classical inputs and outputs—in a composable and statistically secure way, even for a single honest party. The soundness error—the maximum cheating probability of malicious parties—is shown to be proportional to the inverse of a polynomial with respect to the number of rounds in the protocol, and can be further decreased to a negligible quantity for bounded-error quantum-polynomial-time computations. Unlike previous SMPQC protocols, our proposal only requires very limited quantum resources from all but one party. In addition, the protocol exhibits some noise robustness that can facilitate small-scale implementations with near-future technologies. The protocol is based on a new technique for quantum verification that requires only the collective remote preparation of quantum states in a single plane of the Bloch sphere. To demonstrate the ability of verifying the computation with such limited clients, we uncover and use a fundamental invariance that is inherent to measurement-based quantum computing.

DOI
10.1088/2058-9565/adaf12

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Abstract Secure multi-party computation (SMPC) protocols allow several parties distrusting each other to collectively compute a function on their inputs, without revealing the input values. In this paper, we introduce a protocol that lifts SMPC to its quantum counterpart—secure multi-party quantum computation (SMPQC) for classical inputs and outputs—in a composable and statistically secure way, even for a single honest party. The soundness error—the maximum cheating probability of malicious parties—is shown to be proportional to the inverse of a polynomial with respect to the number of rounds in the protocol, and can be further decreased to a negligible quantity for bounded-error quantum-polynomial-time computations. Unlike previous SMPQC protocols, our proposal only requires very limited quantum resources from all but one party. In addition, the protocol exhibits some noise robustness that can facilitate small-scale implementations with near-future technologies. The protocol is based on a new technique for quantum verification that requires only the collective remote preparation of quantum states in a single plane of the Bloch sphere. To demonstrate the ability of verifying the computation with such limited clients, we uncover and use a fundamental invariance that is inherent to measurement-based quantum computing.
Secure multi-party computation (SMPC) protocols allow several parties that distrust each other to collectively compute a function on their inputs. In this paper, we introduce a protocol that lifts classical SMPC to quantum SMPC in a composably and statistically secure way, even for a single honest party. Unlike previous quantum SMPC protocols, our proposal only requires very limited quantum resources from all but one party; it suffices that the weak parties, i.e. the clients, are able to prepare single-qubit states in the X-Y plane. The novel quantum SMPC protocol is constructed in a naturally modular way, and relies on a new technique for quantum verification that is of independent interest. This verification technique requires the remote preparation of states only in a single plane of the Bloch sphere. In the course of proving the security of the new verification protocol, we also uncover a fundamental invariance that is inherent to measurement-based quantum computing.
Multi-Party Quantum Computation (MPQC) has attracted a lot of attention as a potential killer-app for quantum networks through it's ability to preserve privacy and integrity of the highly valuable computations they would enable. Contributing to the latest challenges in this field, we present a composable protocol achieving blindness and verifiability even in the case of a single honest client. The security of our protocol is reduced, in an information-theoretically secure way, to that of a classical composable Secure Multi-Party Computation (SMPC) used to coordinate the various parties. Our scheme thus provides a statistically secure upgrade of such classical scheme to a quantum one with the same level of security. In addition, (i) the clients can delegate their computation to a powerful fully fault-tolerant server and only need to perform single qubit operations to unlock the full potential of multi-party quantum computation; (ii) the amount of quantum communication with the server is reduced to sending quantum states at the beginning of the computation and receiving the output states at the end, which is optimal and removes the need for interactive quantum communication; and (iii) it has a low constant multiplicative qubit overhead compared to the single-client delegated protocol it is built upon. The main technical ingredient of our paper is the bootstraping of the MPQC construction by Double Blind Quantum Computation, a new composable resource for blind multiparty quantum computation, that demonstrates the surprising fact that the full protocol does not require verifiability of all components to achieve security.
Secure Multi-Party Computation (SMPC) aims to enable computation on sensitive data without revealing the individual inputs of the participants. Traditional SMPC protocols often suffer from significant computational overhead, particularly in terms of communication complexity. This paper proposes a novel approach to SMPC leveraging tensor network techniques inspired by quantum computation. We demonstrate that tensor networks can efficiently represent and manipulate the necessary data structures for SMPC protocols, leading to a substantial reduction in communication overhead and improved scalability. Our method utilizes the inherent structure of tensor networks to minimize the number of exchanges required during computation, effectively addressing a key bottleneck in existing SMPC implementations. We outline the theoretical foundations and present a framework for designing SMPC protocols using tensor networks. This work represents a significant step towards practical and efficient SMPC solutions, particularly for large-scale datasets and complex computations. The key contribution lies in the application of quantum-inspired techniques to solve classical computational problems, specifically within the context of secure computation.
We show how to securely realize any multi-party functionality in a way that preserves security under an a-priori bounded number of concurrent executions, regardless of the number of corrupted parties. Previous protocols for the above task either rely on set-up assumptions such as a Common Reference String, or require an honest majority. Our constructions are in the plain model and rely on standard intractability assumptions (enhanced trapdoor permutations and collision resistant hash functions). Even though our main focus is on feasibility of concurrent multi-party computation we actually obtain a protocol using only a constant number of communication rounds. As a consequence our protocol yields the first construction of constant-round phstand-alone secure multi-party computation with a dishonest majority, proven secure under standard (polynomial-time) hardness assumptions; previous solutions to this task either require logarithmic round-complexity, or subexponential hardness assumptions. The core of our protocol is a novel construction of (concurrently) simulation-sound zero-knowledge protocols, which might be of independent interest. Finally, we extend the framework constructed to give a protocol for secure multi-party (and thus two-party) computation for any number of corrupted parties, which remains secure even when arbitrary subsets of parties concurrently execute the protocol, possibly with interchangeable roles. As far as we know, for the case of two-party or multi-party protocols with a dishonest majority, this is the first positive result for any non-trivial functionality which achieves this property in the plain model.
ABSTRACT With the advent of delegated quantum computing as a service, verifying the integrity of quantum computations is becoming a question of great importance. Existing information‐theoretically Secure Delegated Quantum Computing (SDQC) protocols require the client to possess the ability to perform either trusted state preparations or measurements. Whether it is possible to verify universal quantum computations with information‐theoretic security without trusted preparations or measurements was an open question so far. In this paper, we settle this question in the affirmative by presenting a modular, composable, and efficient way to turn known verification schemes into protocols that rely only on trusted gates. Our first contribution is an extremely lightweight reduction of the problem of quantum verification for to the trusted application of single‐qubit rotations around the axis and bit flips. The second construction presented in this work shows that it is possible to information‐theoretically verify arbitrary quantum computations without trusted preparations or measurements if the verifier can perform two‐qubit gates on a register whose size is logarithmic in the security parameter. Our third contribution extends these two results to the multi‐party setting in which multiple mutually distrustful clients delegate a joint computation to a potentially malicious server.
We show that a classical client with no quantum hardware can use a single untrusted and potentially malicious quantum server as if it were its own trusted quantum computer. Through the server, the client can privately choose and run quantum computations, prepare quantum states, and process quantum states supplied by other parties. It can also keep quantum memory on the server, hidden from the server itself, and use that memory in later computations so its quantum state persists across rounds of interaction. Together, these capabilities let a purely classical party act as a quantum party in a variety of interactive protocols. We expect this virtual quantum computer to be a broadly useful tool. As immediate applications, we resolve two known open problems: (1) classical verification of quantum sampling with negligible computational soundness error, and (2) remote state preparation of arbitrary efficiently preparable quantum states. Underlying all of these results is a general-purpose, maliciously secure two-party computation protocol between a classical client and a quantum server, which we construct assuming only the post-quantum hardness of learning with errors.