Simplemindedly, a number theoretic transform is a generalization of a fast Fourier transform obtained by replacing 
with an 
th primitive root of unity.
This effectively means doing a transform over the quotient
ring 
instead of the complex numbers 
. The theory is rather elegant and uses the language of finite fields and number
theory.
Number Theoretic Transform
See also
Fast Fourier Transform, Finite FieldExplore with Wolfram|Alpha
References
Arndt, J. "Numbertheoretic Transforms (NTTs)." Ch. 4 in "Remarks on FFT Algorithms." http://www.jjj.de/fxt/.Cohen, H. A Course in Computational Algebraic Number Theory. New York: Springer-Verlag, 1993.Referenced on Wolfram|Alpha
Number Theoretic TransformCite this as:
Weisstein, Eric W. "Number Theoretic Transform." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NumberTheoreticTransform.html