Description: to multiply the "complex unit" $w^{N/4}$ over a prime field, i.e., $w^N \equiv 1 \bmod (\,p)$ (suppose $p, N$ do provide such primitive root).
- I am implementing the radix-4 Number Theoretic Transform which involves the multiplications with the complex unit "$j$".
- It seems that in the complex domain, multiplication with the complex unit is "almost" free, i.e., $a + bj \to -b + aj$. That is one of the reasons that radix-4 FFT can save more number of multiplications compared with the radix-2 implementation.
- However, over the prime field, I have no idea whether this free multiplication is possible or not.
Thanks.