结合超椭圆曲线密码学和格分析宽度-w非邻接形式
Analysis of the Width-w Non-Adjacent Form in Conjunction with Hyperelliptic Curve Cryptography and with Lattices
摘要：
我们分析了一个固定的非零数字的出现次数的宽度-W非相邻形式的所有元素的晶格在某些区域（例如，一个球）。我们的结果是一个渐近公式，其主项与完整的分组长度分析一致。在其第二阶项的周期性波动表现出来。证明遵循Delange的方法。这个结果在一般的格设置，然后用于数字系统的代数整数作为基地。这些结果来自于超椭圆曲线密码学中有效的标量乘法（Frobenius-and-add方法），我们的结果对于分析此类算法的运行时间是必要的。
英文摘要：
We analyse the number of occurrences of a fixed non-zero digit in the width-w non-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 the full block length analysis. In its second order term a periodic fluctuation is exhibited. The proof follows Delange's method. This result in a general lattice set-up is then used for numeral systems with an algebraic integer as base. Those come from efficient scalar multiplication methods (Frobenius-and-add methods) in hyperelliptic curves cryptography, and our result is needed for analysing the running time of such algorithms.
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