Using the smoothness of p-1 for computing roots modulo p

Bartosz Zralek

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arXiv · 0803.0471

Using the smoothness of p-1 for computing roots modulo p

Bartosz Zralek

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Abstract

We prove, without recourse to the Extended Riemann Hypothesis, that the projection modulo $p$ of any prefixed polynomial with integer coefficients can be completely factored in deterministic polynomial time if $p-1$ has a $(\ln p)^{O(1)}$-smooth divisor exceeding $(p-1)^{{1/2}+δ}$ for some arbitrary small $δ$. We also address the issue of computing roots modulo $p$ in deterministic time.

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Bartosz Zralek. 2008-03-04. Using the smoothness of p-1 for computing roots modulo p. https://arxiv.org/abs/0803.0471

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