Multiply Numbers using Number Theoretic Transform

Multiply very numbers (hexadecimal or decimal) together efficiently using Number Theoretic Transform (NTT)

Large Number Multiplier using Number Theoretic Transform (NTT). Quickly multiply two large numbers (either hexadecimal numbers or decimal numbers) together (less than approximately 500,000 (32-bit segments). Inputs to the multiply() function must be hexadecimal or decimal character arrays of at least 6 characters in length. Size can be up to 4 million characters each. The NTT should provide exact results (tested on several large inputs). I went through this exercise to learn about the NTT process and how it works. Output is of the same form as the input, either hexadecimal or decimal.

For example (inputs could be significantly larger):

a='1a2b3c4e5678987691827364abcdef1234567821123aabbcceeddff463723892736452';
b='9a8b7c6d5e4f123456473829ffddee1ffeeddaaccbb238edf1823938473627837463562aabbccddeeff2345678';
c=multiply(a,b);

Output:
c= '0fcc4478fdd013c81ae05b64c7bb3684de2ad903235d1f77200b0ccd60bc2ae10de191b86350c54c3632506364fd269e2bb91f08ffaf90110e75d19a688b025f5ad2ffe39f408feafd4f248b4e729270'

a='198583931643537581442143136962572284781970832530224711489217605344156699047702520914';
b='1417793757582264142991820210002764610425931296836066215122869608550065190067340067192259569688783751463851640';
Output:
c='281551058640350635133920212774963620686487650950043670801076786888070561874593787199498117484873007760364284017039572666137806333241698549708893818835351498777984006753645623564120972093198960'