Private computation is a generalization of private information retrieval, in which a user is able to compute a function on a distributed dataset without revealing the identity of that function to the servers. In this paper, it is shown that Lagrange encoding, a powerful technique for encoding Reed-Solomon codes, enables private computation in many cases of interest. In particular, we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data, while being robust to Byzantine and straggling servers, and to servers colluding to attempt to deduce the identities of the functions to be evaluated. Moreover, incorporating ideas from the well-known Shamir secret sharing scheme allows the data itself to be concealed from the servers as well. Our results extend private computation to high degree polynomials and to data-privacy, and reveal a tight connection between private computation and coded computation.

中文翻译：

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拉格朗日编码的私有多项式计算

私有计算是私有信息检索的一般化，其中用户能够在分布式数据集上计算功能，而无需向服务器透露该功能的身份。在本文中，我们证明了Lagrange编码是一种强大的Reed-Solomon码编码技术，可以在许多感兴趣的情况下进行私有计算。尤其是，我们提出了一种方案，该方案能够对Lagrange编码数据进行任意程度的多项式私有计算，同时对拜占庭式服务器和散乱的服务器以及合谋尝试推论要评估的功能的服务器具有鲁棒性。此外，结合著名的Shamir秘密共享方案的思想，还可以将数据本身也隐藏在服务器之外。