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We analyse the number of occurrences of a fixed non-zero digit in the width-wnon-adjacent forms of all elements of a lattice in some region (e.g. a ball).Our result is an asymptotic formula, where its main term coincides with thefull block length analysis. In its second order term a periodic fluctuation isexhibited. The proof follows Delange's method. This result in a general latticeset-up is then used for numeral systems with an algebraic integer as base.Those come from efficient scalar multiplication methods (Frobenius-and-addmethods) in hyperelliptic curves cryptography, and our result is needed foranalysing the running time of such algorithms.

Analysis of the Width-w Non-Adjacent Form in Conjunction with Hyperelliptic Curve Cryptography and with Lattices