Closed-Form Orthogonal Number Theoretic Transform Eigenvectors and the Fast Fractional NTT

@article{Pei2011ClosedFormON,
  title={Closed-Form Orthogonal Number Theoretic Transform Eigenvectors and the Fast Fractional NTT},
  author={Soo-Chang Pei and Chia-Chang Wen and Jian-Jiun Ding},
  journal={IEEE Transactions on Signal Processing},
  year={2011},
  volume={59},
  pages={2124-2135}
}
In this paper, we propose a new method to find the closed-form solution of Number Theoretic Transform (NTT) eigenvectors. We construct the complete generalized Legendre sequence over the finite field (CGLSF) and use it to solve the NTT eigenvector problem. We derive the CGLSF-like NTT eigenvectors successfully, including the case where the operation field is defined over the Fermat and Mersenne numbers. The derived NTT eigenvector set is orthogonal and has a closed form. It is suitable for… CONTINUE READING

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