### A linear time algorithm for residue computation and a fast algorithm for division with a sparse divisorA linear time algorithm for residue computation and a fast algorithm for division with a sparse divisor

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 Author Kaminski, Michael Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1987 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract An algorithm is presented to compute the residue of a polynomial over a finite field of degree $\textit{n}$ modulo a polynomial of degree $\textit{O}(log$ $\textit{n})$ in $\textit{O}(\textit{n})$ algebraic operations. This algorithm can be implemented on a Turing machine. The implementation is based on Turing machine procedure that divides a polynomial of degree $\textit{n}$ by a sparse polynomial with $\textit{k}$ nonzero coefficients in $\textit{O}(\textit{kn})$ steps. This algorithm can be adapted to compute the residue of a number of length $\textit{n}$ modulo a number of length $\textit{O}(log$ $\textit{n})$ in $\textit{O}(\textit{n})$ bit operations. 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 1987-10-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 34 Issue Number 4 Page Count 17 Starting Page 968 Ending Page 984

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Source: ACM Digital Library