Accelerating Number Theoretic Transformations for Bootstrappable Homomorphic Encryption on GPUs

Understand

Homomorphic encryption (HE) draws huge attention as it provides a way of privacy-preserving computations on encrypted messages.

• Number Theoretic Transform (NTT), a specialized form of Discrete Fourier Transform (DFT) in the finite field of integers, is the key algorithm that enables fast computation on encrypted ciphertexts in HE.
• Prior works have accelerated NTT and its inverse transformation on a popular parallel processing platform, GPU, by leveraging DFT optimization techniques.
• However, these GPU-based studies lack a comprehensive analysis of the primary differences between NTT and DFT or only consider small HE parameters that have tight constraints in the number of arithmetic operations that can be performed without decryption.