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.

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