Differentially Private Distributed Matrix Multiplication: Fundamental Accuracy-Privacy Trade-Off Limits
Differentially Private Distributed Matrix Multiplication: Fundamental Accuracy-Privacy Trade-Off Limits
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DOI：
10.1109/isit50566.2022.9834493
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发表时间：
2022-06
期刊：
影响因子：
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通讯作者：
A. Devulapalli;V. Cadambe;F. Calmon;Haewon Jeong
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文献类型：
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作者：
A. Devulapalli;V. Cadambe;F. Calmon;Haewon Jeong
Ben Or，Goldwasser和Wigderson提出的安全多方计算的经典BGW算法证明了有限域上的安全分布式矩阵乘法在2 t +1个计算节点上是可能的，同时对每t个合谋计算节点保持输入矩阵的私有性。在本文中，我们开发和研究了一种新的编码公式，探索在安全多方计算的实值数据，即使少于2 t +1个节点，通过差分隐私的角度计算精度和隐私之间的权衡。对于t = 1的情况下，我们开发了可实现的方案和匡威的参数，约束的隐私-差分隐私参数，测量隐私损失-对于给定的准确度水平。我们实现的编码方案是沙米尔秘密共享应用于实值数据的专业化，再加上适当的选择评估点。我们开发的匡威参数，适用于一般的加性噪声为基础的计划。
The classic BGW algorithm of Ben Or, Goldwasser and Wigderson for secure multiparty computing demonstrates that secure distributed matrix multiplication over finite fields is possible over 2t+1 computation nodes, while keeping the input matrices private from every t colluding computation nodes. In this paper, we develop and study a novel coding formulation to explore the trade-offs between computation accuracy and privacy in secure multiparty computing for real-valued data, even with fewer than 2t+1 nodes, through a differential privacy perspective. For the case of t = 1, we develop achievable schemes and converse arguments that bound ϵ — the differential privacy parameter that measures the privacy loss — for a given accuracy level. Our achievable coding schemes are specializations of Shamir secret sharing applied to real-valued data, coupled with appropriate choice of evaluation points. We develop converse arguments that apply for general additive noise based schemes.