Affiliation:
1. Univ. of Toronto, Toronto, Ont., Canada
2. IBM T.J. Watson Research Center, Yorktown Heights, NY
Abstract
Modular integer exponentiation (given
a, e,
and
m
, compute
a
e
mod
m
) is a fundamental problem in algebraic complexity for which no efficient parallel algorithm is known. Two closely related problems are modular polynomial exponentiation (given
a
(
x
),
e
, and
m
(
x
), compute (
a
(
x
))
e
mod
m
(
x
)) and polynomial exponentiation (given
a
(
x
),
e
. and
t
, compute the coefficient of
x
t
in (
a
(
x
))
e
). It is shown that these latter two problems are in
NC
2
when
a
(
x
) and
m
(
x
) are polynomials over a finite field whose characteristic is polynomial in the input size.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
20 articles.
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