Fast number theory Transformation (NTT)--study notes

NTT

Aw, it's simple.

The FFT F-F-T FFT can be accelerated due to the good nature of having the primary n units root wn=e2πin w n = e 2πi n w_n=e^{\frac{2\pi i}{n}}. In the natural number field, modulo p p p, the WN w n w_n can be replaced with gp−1n g p−1 n G^{\frac{p-1}{n}}, G G g is the root of P p p, it can be found that those properties are similar. The inverse transformation also converts gp−1n g p−1 n G^{\frac{p-1}{n}} to g−p−1n g−p−1 n g^{-\frac{p-1}{n}, and then divides the last by N n N.

To be able to NTT, it is necessary to satisfy the modulus P p p is prime and p−1 p−1 P-1 is a multiple of n n N (2 recurses). So p p p should generally be