In this thesis, we are mainly interested in constructing deterministic polynomial-time algorithms for solving some computational problems that arise in number theory and cryptography. The problems we are interested in include finite field arithmetic, primality testing, and elliptic curve arithmetic.In this case, for any q = pn = 2625e5t+ 1 with t = poly (log q), taking square roots in Ayq can be done in polynomial time. 2.4.3 Computing C23H1 Suppose p be a prime with p = 1 (mod 4) and p = 4, 7 (mod 9). We show in Lemma 2.4.7 belowanbsp;...

Title | : | On Solving Univariate Polynomial Equations Over Finite Fields and Some Related Problems |

Author | : | |

Publisher | : | ProQuest - 2007 |

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