Performance Increasing Approaches For Binary Field Inversion

Authors propose several approaches for increasing performance of multiplicative inversion algorithm in binary fields based on Extended Euclidean Algorithm (EEA). First approach is based on Extended Euclidean Algorithm specificity: either invariant polynomial v remains intact or swaps with invariant polynomial u . It makes it possible to avoid necessity of polynomial v degree computing. The second approach is based on searching the "next matching index" when calculating the degree of the polynomial, since degree polynomial invariant u at least decreases by 1, then it is possible to use current value while further calculation the degree of the polynomial.