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A fast algorithm for polynomial factorization over p

David FordSebastian PauliXavier-François Roblot — 2002

Journal de théorie des nombres de Bordeaux

We present an algorithm that returns a proper factor of a polynomial Φ ( x ) over the p -adic integers p (if Φ ( x ) is reducible over p ) or returns a power basis of the ring of integers of p [ x ] / Φ ( x ) p [ x ] (if Φ ( x ) is irreducible over p ). Our algorithm is based on the Round Four maximal order algorithm. Experimental results show that the new algorithm is considerably faster than the Round Four algorithm.

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