Homomorphic Encryption (HE) allows any third party to operate on the encrypted data without decrypting it in advance. For the majority of HE schemes, the multiplicative depth of circuits is the main practical limitation in performing computations over encrypted data. Hence, Homomorphic multiplication is one of the most important components of homomorphic encryption. Since most of the HE schemes are constructed from the ring-learning with errors (R-LWE) problem. Efficient polynomial modular multiplication implementation becomes critical. This work consists of describing various approaches to implementing polynomial modular multiplication based on number theoretic transform.

翻译：同态加密（Homomorphic Encryption，HE）允许任何第三方在不预先解密的情况下对加密数据进行操作。对于大多数同态加密方案而言，电路的乘法深度是在加密数据上执行计算的主要实际限制。因此，同态乘法是同态加密最重要的组成部分之一。由于大多数同态加密方案基于环学习误差（Ring-Learning with Errors，R-LWE）问题构建，高效的多项式模乘法实现变得至关重要。本工作旨在描述基于数论变换的多项式模乘法的各种实现方法。