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.Like the relationship between taking square roots and constructing quadratic nonresidues, the problem of ... positive integer and r not the characteristic of the field, is polynomial time reducible to the problem of taking rth roots, and vice versa.
|Title||:||On Solving Univariate Polynomial Equations Over Finite Fields and Some Related Problems|
|Author||:||Tsz Wo Sze|
|Publisher||:||ProQuest - 2007|