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AbstractÐA fast algorithm for multiplicative inversion in qp P m using normal basis is proposed. It is an improvement on those proposed by Itoh and Tsujii and by Chang et al., which are based on Fermat's Theorem and require ylog m multiplications. The number of multiplications is reduced by decomposing m À I into several factors and a small remainder. Index TermsÐFinite field, finite field inversion, Fermat's theorem, normal basis.doi:10.1109/12.926155 fatcat:vwguckgirjb6joon5zmt3yoyum