Zhang Yiran, Geng Huizheng, Su Li, He Shen, Lu Li
China Mobile Research Institute, Beijing, 100053, China.
Sci Rep. 2024 Apr 12;14(1):8512. doi: 10.1038/s41598-024-53267-x.
With the development of cloud computing, users are more inclined to outsource complex computing tasks to cloud servers with strong computing capacity, and the cloud returns the final calculation results. However, the cloud is not completely trustworthy, which may leak the data of user and even return incorrect calculations on purpose. Therefore, it is important to verify the results of computing tasks without revealing the privacy of the users. Among all the computing tasks, the polynomial calculation is widely used in information security, linear algebra, signal processing and other fields. Most existing polynomial-based verifiable computation schemes require that the input of the polynomial function must come from a single data source, which means that the data must be signed by a single user. However, the input of the polynomial may come from multiple users in the practical application. In order to solve this problem, the researchers have proposed some schemes for multi-source outsourced data, but these schemes have the common problem of low efficiency. To improve the efficiency, this paper proposes an efficient polynomial-based verifiable computation scheme on multi-source outsourced data. We optimize the polynomials using Horner's method to increase the speed of verification, in which the addition gate and the multiplication gate can be interleaved to represent the polynomial function. In order to adapt to this structure, we design the corresponding homomorphic verification tag, so that the input of the polynomial can come from multiple data sources. We prove the correctness and rationality of the scheme, and carry out numerical analysis and evaluation research to verify the efficiency of the scheme. The experimental indicate that data contributors can sign 1000 new data in merely 2 s, while the verification of a delegated polynomial function with a power of 100 requires only 18 ms. These results confirm that the proposed scheme is better than the existing scheme.
随着云计算的发展，用户更倾向于将复杂的计算任务外包给具有强大计算能力的云服务器，然后云服务器返回最终的计算结果。然而，云并非完全可信，它可能会泄露用户数据，甚至故意返回错误的计算结果。因此，在不泄露用户隐私的情况下验证计算任务的结果非常重要。在所有计算任务中，多项式计算在信息安全、线性代数、信号处理等领域有着广泛的应用。大多数现有的基于多项式的可验证计算方案要求多项式函数的输入必须来自单一数据源，这意味着数据必须由单个用户签名。然而，在实际应用中，多项式的输入可能来自多个用户。为了解决这个问题，研究人员提出了一些针对多源外包数据的方案，但这些方案都存在效率低下的共同问题。为了提高效率，本文提出了一种基于多源外包数据的高效多项式可验证计算方案。我们使用霍纳法则优化多项式以提高验证速度，其中加法门和乘法门可以交错排列来表示多项式函数。为了适应这种结构，我们设计了相应的同态验证标签，使得多项式的输入可以来自多个数据源。我们证明了该方案的正确性和合理性，并进行了数值分析和评估研究以验证该方案的效率。实验表明，数据贡献者仅需2秒就能签署1000条新数据，而验证幂次为(100)的委托多项式函数仅需(18)毫秒。这些结果证实了所提出的方案优于现有方案。
