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As homework, I should implement integer multiplication on numbers of a 1000 digits using a divide and conquer approach that works below O(n). What algorithm should I look into?
Schönhage–Strassen algorithm is the one of the fastest multiplication algorithms known. It takes O(n log n log log n) time.
Fürer’s algorithm is the fastest large number multiplication algorithm known so far and takes O(n*log n * 2O(log*n)) time.
I don’t think any multiplication algorithm could take less than or even equal to O(n). That’s simply not possible.