International Association
for Cryptologic Research

In this paper, we study the distribution of the \textit{gap} between terms in an addition chain. In particular, we show that if $1,2,\ldots,s_{\delta(n)}=n$ is an addition chain of length $\delta(n)$ leading to $n$, then $$\underset{1\leq l\leq \delta(n)}{\mathrm{sup}}(s_{l+k}-s_l)\gg k\frac{n}{\delta(n)}$$ and $$\underset{1\leq l\leq \delta(n)}{\mathrm{inf}}(s_{l+k}-s_l)\ll k\frac{n}{\delta(n)}$$ for fixed $k\geq 1$.