Homomorphic encryption, which enables the execution of arithmetic operations directly on ciphertexts, is a promising solution for protecting privacy of cloud-delegated computations on sensitive data. However, the correctness of the computation result is not ensured. We propose two error detection encodings and build authenticators that enable practical client-verification of cloud-based homomorphic computations under different trade-offs and without compromising on the features of the encryption algorithm. Our authenticators operate on top of trending ring learning with errors based fully homomorphic encryption schemes over the integers. We implement our solution in VERITAS, a ready-to-use system for verification of outsourced computations executed over encrypted data. We show that contrary to prior work VERITAS supports verification of any homomorphic operation and we demonstrate its practicality for various applications, such as ride-hailing, genomic-data analysis, encrypted search, and machine-learning training and inference.

翻译：同态加密支持直接在密文上执行算术运算，是保护云端敏感数据计算隐私的一种有前景的解决方案。然而，计算结果正确性无法得到保证。我们提出了两种错误检测编码，并构建了验证器，能够在不同权衡条件下实现对云端同态计算的实用客户端验证，且不损害加密算法的功能特性。我们的验证器基于当前流行的基于整数上带误差环学习的全同态加密方案进行构建。我们将解决方案实现于VERITAS系统中——这是一个可直接使用的系统，用于验证在加密数据上执行的外包计算。研究表明，与先前工作不同，VERITAS支持验证任意同态运算，并展示了其在各种应用场景中的实用性，如网约车、基因组数据分析、加密搜索以及机器学习训练与推理。