Paper 2025/049 Original: eprint.iacr.org/2025/049 ↗
On the gap between terms in an addition chain
Abstract
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 $k\geq 1$.
Metadata
- Available format(s)
PDF- Category
- Applications
- Publication info
- Preprint.
- History
- 2025-01-13: last updated
- 2025-01-13: published
- Short URL
- https://ia.cr/2025/049
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2025/049,
author = {Theophilus Agama},
title = {On the gap between terms in an addition chain},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/049},
year = {2025},
url = {https://eprint.iacr.org/2025/049}
}