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We initiate the study of multi-party computation for classical functionalities (in the plain model) with security against malicious polynomial-time quantum adversaries. We observe that existing techniques readily give a polynomial-round protocol, but our main result is a construction of *constant-round* post-quantum multi-party computation. We assume mildly super-polynomial quantum hardness of learning with errors (LWE), and polynomial quantum hardness of an LWE-based circular security assumption. Along the way, we develop the following cryptographic primitives that may be of independent interest: 1. A spooky encryption scheme for relations computable by quantum circuits, from the quantum hardness of an LWE-based circular security assumption. This yields the first quantum multi-key fully-homomorphic encryption scheme with classical keys. 2. Constant-round zero-knowledge secure against multiple parallel quantum verifiers from spooky encryption for relations computable by quantum circuits. To enable this, we develop a new straight-line non-black-box simulation technique against *parallel* verifiers that does not clone the adversarys state. This forms the heart of our technical contribution and may also be relevant to the classical setting. 3. A constant-round post-quantum non-malleable commitment scheme, from the mildly super-polynomial quantum hardness of LWE.
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Quantum conference is a process of securely exchanging messages between three or more parties, using quantum resources. A Measurement Device Independent Quantum Dialogue (MDI-QD) protocol, which is secure against information leakage, has been proposed (Quantum Information Processing 16.12 (2017): 305) in 2017, is proven to be insecure against intercept-and-resend attack strategy. We first modify this protocol and generalize this MDI-QD to a three-party quantum conference and then to a multi-party quantum conference. We also propose a protocol for quantum multi-party XOR computation. None of these three protocols proposed here use entanglement as a resource and we prove the correctness and security of our proposed protocols.
We consider the task of secure multi-party distributed quantum computation on a quantum network. We propose a protocol based on quantum error correction which reduces the number of necessary qubits. That is, each of the $n$ nodes in our protocol requires an operational workspace of $n^2 + 4n$ qubits, as opposed to previously shown $Omegabig((n^3+n^2s^2)log nbig)$ qubits, where $s$ is a security parameter. Additionally, we reduce the communication complexity by a factor of $mathcal{O}(n^3log(n))$ qubits per node, as compared to existing protocols. To achieve universal computation, we develop a distributed procedure for verifying magic states, which allows us to apply distributed gate teleportation and which may be of independent interest. We showcase our protocol on a small example for a 7-node network.
I construct a secure multi-party scheme to compute a classical function by a succinct use of a specially designed fault-tolerant random polynomial quantum error correction code. This scheme is secure provided that (asymptotically) strictly greater than five-sixths of the players are honest. Moreover, the security of this scheme follows directly from the theory of quantum error correcting code, and hence is valid without any computational assumption. I also discuss the quantum-classical complexity-security tradeoff in secure multi-party computation schemes and argue why a full-blown quantum code is necessary in my scheme.
Secure multi-party computation (MPC) allows parties to perform computations on data while keeping that data private. This capability has great potential for machine-learning applications: it facilitates training of machine-learning models on private data sets owned by different parties, evaluation of one partys private model using another partys private data, etc. Although a range of studies implement machine-learning models via secure MPC, such implementations are not yet mainstream. Adoption of secure MPC is hampered by the absence of flexible software frameworks that speak the language of machine-learning researchers and engineers. To foster adoption of secure MPC in machine learning, we present CrypTen: a software framework that exposes popular secure MPC primitives via abstractions that are common in modern machine-learning frameworks, such as tensor computations, automatic differentiation, and modular neural networks. This paper describes the design of CrypTen and measure its performance on state-of-the-art models for text classification, speech recognition, and image classification. Our benchmarks show that CrypTens GPU support and high-performance communication between (an arbitrary number of) parties allows it to perform efficient private evaluation of modern machine-learning models under a semi-honest threat model. For example, two parties using CrypTen can securely predict phonemes in speech recordings using Wav2Letter faster than real-time. We hope that CrypTen will spur adoption of secure MPC in the machine-learning community.
In this work, we consider the problem of secure multi-party computation (MPC), consisting of $Gamma$ sources, each has access to a large private matrix, $N$ processing nodes or workers, and one data collector or master. The master is interested in the result of a polynomial function of the input matrices. Each source sends a randomized functions of its matrix, called as its share, to each worker. The workers process their shares in interaction with each other, and send some results to the master such that it can derive the final result. There are several constraints: (1) each worker can store a function of each input matrix, with the size of $frac{1}{m}$ fraction of that input matrix, (2) up to $t$ of the workers, for some integer $t$, are adversary and may collude to gain information about the private inputs or can do malicious actions to make the final result incorrect. The objective is to design an MPC scheme with the minimum number the workers, called the recovery threshold, such that the final result is correct, workers learn no information about the input matrices, and the master learns nothing beyond the final result. In this paper, we propose an MPC scheme that achieves the recovery threshold of $3t+2m-1$ workers, which is order-wise less than the recovery threshold of the conventional methods. The challenge in dealing with this set up is that when nodes interact with each other, the malicious messages that adversarial nodes generate propagate through the system, and can mislead the honest nodes. To deal with this challenge, we design some subroutines that can detect erroneous messages, and correct or drop them.
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