Constructing Nonresidues in Finite Fields and
نویسندگان
چکیده
We describe a new deterministic algorithm for the problem of constructing k-th power nonresidues in nite elds GF(p n), where p is prime and k is a prime divisor of p n ?1. We prove under the assumption of the Extended Riemann Hypothesis (ERH), that for xed n and p ! 1, our algorithm runs in polynomial time. Unlike previous algorithms for this problem, this polynomial time bound holds even if k is very large. More generally, assuming the ERH, in time (log p) O(n) we can construct a set of elements that generates GF(p n) .
منابع مشابه
Constructing Nonresidues in Finite Fields and the Extended Riemann Hypothesis February
We describe a new deterministic algorithm for the problem of constructing k th power nonresidues in nite elds GF p where p is prime and k is a prime divisor of p We prove under the assumption of the Extended Riemann Hypothesis ERH that for xed n and p our algorithm runs in polynomial time Unlike previous algorithms for this problem this polynomial time bound holds even if k is very large More g...
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