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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

5
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Take a look at these papers from Dan Bernstein. It's not quite what you are looking for, but he does even more than you need in time $n(\lg n)^{2+o(1)}$ where $n$ = number of bits of $N\cdot d$ (one o …
answered May 6 '10 by Someone
2
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A good source for highly efficient algorithms and implementations for this kind of problems is Dan Bernstein's homepage. There I found an algorithms that might be useful for weeding out all the small …
answered Nov 22 '12 by Someone