The parallel complexity of exponentiating polynomials over finite fields

Modular integer exponentiation (given a, e, and m, compute ae 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 xt in (a(x))e). It is shown that these latter two problems are in NC2 when a(x) and m(x) are polynomials over a finite field whose characteristic is polynomial in the input size. © 1988, ACM. All rights reserved.