### The parallel complexity of exponentiating polynomials over finite fieldsThe parallel complexity of exponentiating polynomials over finite fields

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 Author Fich, Faith E. ♦ Tompa, Martin Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1988 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract Modular integer exponentiation (given a, e, and $\textit{m},$ compute $\textit{a}e$ mod $\textit{m})$ is a fundamental problem in algebraic complexity for which no efficient parallel algorithm is known. Two closely related problems are modular polynomial exponentiation (given $\textit{a}(\textit{x}),$ $\textit{e},$ and $\textit{m}(\textit{x}),$ compute $(\textit{a}(\textit{x}))e$ mod $\textit{m}(\textit{x}))$ and polynomial exponentiation (given $\textit{a}(\textit{x}),$ $\textit{e}.$ and $\textit{t},$ compute the coefficient of $\textit{xt}$ in $(\textit{a}(\textit{x}))e).$ It is shown that these latter two problems are in $\textit{NC}2$ when $\textit{a}(\textit{x})$ and $\textit{m}(\textit{x})$ are polynomials over a finite field whose characteristic is polynomial in the input size. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1988-06-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 35 Issue Number 3 Page Count 17 Starting Page 651 Ending Page 667

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Source: ACM Digital Library