In this study, we propose a two-party computation protocol for approximate matrix multiplication of fixed-point numbers. The proposed protocol is provably secure under standard lattice-based cryptographic assumptions and enables matrix multiplication at a desired approximation level within a single round of communication. We demonstrate the feasibility of the protocol by applying it to the secure implementation of a linear control law. Our evaluation reveals that the client achieves lower online computational complexity compared to the original controller computation, while ensuring the privacy of controller inputs, outputs, and parameters. Furthermore, a numerical example confirms that the proposed method maintains sufficient precision of control inputs even in the presence of approximation and quantization errors.

翻译：本研究提出了一种用于定点数近似矩阵乘法的两方计算协议。该协议在标准格基密码学假设下具有可证明安全性，并能在单轮通信内以期望的近似精度实现矩阵乘法。我们通过将其应用于线性控制律的安全实现，验证了该协议的可行性。评估结果表明，与原始控制器计算相比，客户端实现了更低的在线计算复杂度，同时保证了控制器输入、输出和参数的隐私性。此外，数值实例证实，即使在存在近似误差和量化误差的情况下，所提方法仍能保持控制输入的足够精度。