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22L−i . Representation and basic operations modulo M . We clarify how numbers in ZM are represented. Let 2L ≡ −1(mod M ) be denoted with the special symbol 1. We represent each element of ZM \ {1} in the expected way, as a binary string (bL−1 , . . , b0 ) of length L; the element 1 is given a special representation. For example, with M = 17, L = 4 then 13 is represented by (1, 1, 0, 1), or simply written as (1101). , O(L) time. Of course, special considerations apply to 1. 1: Show that addition and subtraction take O(L) bit operations.

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Fundamental problems of algorithmic algebra (draft) by Chee-Keng Yap

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