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Hensel’s lifting

The Programming Works – Number theory is full of gems that turn into effective algorithms demanded in cryptography. Consider the congruence where N is odd, and R > N is a power of 2. Probably the most effective algorithm to solve it is based on the Hensel’s lemma; the corollary that applies for our congruence is: suppose we know the solution for : then the solution for is either or Example: solve We start with the trivial which can be nothing else but ; next, which can be either or ; checking the first alternative gives , so ; next, ; checking gives , so ; next, ; checking gives , so ; finally, ...
Favorite? Off-Topic? Serg @ 2016-05-02 14:15

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