Affiliation:
1. Illinois Wesleyan University, Park St. Bloomington, IL
Abstract
This article explores the asymptotic complexity of two problems related to the Miller-Rabin-Selfridge primality test. The first problem is to tabulate strong pseudoprimes to a single fixed base
a
. It is now proven that tabulating up to
x
requires
O
(
x
) arithmetic operations and
O
(
x
log
x
) bits of space. The second problem is to find all strong liars and witnesses, given a fixed odd composite
n
. This appears to be unstudied, and a randomized algorithm is presented that requires an expected
O
((log
n
)
2
+ |
S
(
n
)|) operations (here
S
(
n
) is the set of strong liars). Although interesting in their own right, a notable application is the search for sets of composites with no reliable witnesses.
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)