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：

---

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概括，其中用户能够在分布式数据集上计算函数，而无需向服务器透露该函数的身份。本文表明，拉格朗日编码是一种用于编码里德所罗门码的强大技术，可以在许多感兴趣的情况下实现私有计算。特别是，我们提出了一种方案，可以对拉格朗日编码数据进行任意次数的多项式的私有计算，同时对拜占庭和落后的服务器以及串通试图推断要评估的函数的身份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，也可以对服务器隐藏数据本身。我们的结果将私有计算扩展到高次多项式和数据隐私，并揭示了私有计算和编码计算之间的紧密联系。