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Lecture notes in computer science

Efficient Large-Scale Multi-party Computation Based on Garbled Circuit

Zhusen Liu, Jiafei Wu, Zhe Liu

Published Oct 24, 2024• 1 citation
Publisher
DOI
10.1007/978-981-97-9053-1_14

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Secure Multi-party Computation (SMC) has been introduced to allow the computation of generic functions between two parties that want to keep secret the input they use, and share only the computed result. One of the approach proposed to solve the SMC problem relies on the design of Garbled Circuits (GC), that are Boolean circuits that can be evaluated collaboratively achieving the SMC goal. Recently, there is a growing interest on the efficiency of this technique and on its potential applications to computation outsourcing in untrusted environments. One of the possible ways to reduce the complexity of the computation is to lower the number of non-EXOR gates in the Boolean circuit, since those gates have no cost for the execution of the secure computation protocol. In this work, we discuss the possibility to construct Garbled Circuit using quantum gates (QG), observing that, in some cases, the quantum GC requires a lower number of non-EXOR gates with respect to the corresponding classical GC implementations, thus improving the overall efficiency of the execution of the SMC protocol.
Secure Multi-party Computation (SMC) is a classical problem in theoretical security. In a SMC problem, two or more parties must compute correctly a function f on their respective inputs x and y, while preserving the privacy of their inputs and additional security properties. One of the approaches proposed for addressing the SMC problem relies on the design of Garbled Circuit (GC). In Garbled Circuits (GCs), the function to be computed is represented as a Boolean circuit composed of binary gates. The input and output wire of each gate is masked such that the party evaluating the Garbled Boolean Circuits (GBC) cannot gain any information about the inputs or the intermediate results that appear during the function evaluation. The complexity of today's most efficient GC protocol depends linearly on the size of the Boolean circuit representation of the evaluated function. The total cost and run-time interaction between parties increase linearly with the number of gates and can be huge for complex GBCs. Actually, interest has grown in the efficiency of this technique and in its applications to computation outsourcing in untrusted environments. A recent work shows that XOR gates in a Boolean circuit have no cost for the secure computation protocol. Therefore, circuits with a reduced number of non-XOR gates are more convenient and one of the possible ways to reduce the complexity of the computation is to reduce the number of non-XOR gates in the Boolean circuit. Recalling that, the main aim of this work is to reduce the number of non-XOR gates, which directly results in a reduced number of interactions between the parties and transfer complexity at runtime, we present different approaches for reducing the communication cost of Secure Multi-party Computation (SMC) and improving the overall computation time and efficiency of the execution of SMC.
Two-party Secure Multi-party Computation (SMC) is a classical problem in theoretical security. The Garbled Circuit (GC) approach has been proposed as a method for solving SMC using Boolean circuits. Actually, interest has grown in the efficiency of this technique and in its applications to computation outsourcing in untrusted environments. A recent work shows that EXOR gates in a Boolean circuit have no cost for the secure computation protocol. Therefore, circuits with a reduced number of non-EXOR gates are more convenient. In this work, we discuss Garbled Circuit construction for two-party secure function evaluation using quantum gates (QG). We observe that, in some cases, the quantum GC involves a lower number of non-EXOR gates than the corresponding classical GC implementations, resulting in a reduced cost in terms of Oblivious Transfer (OT) communication at runtime.