Paper 2023/020
The Scholz conjecture on addition chain is true for infinitely many integers with ℓ(2n) = ℓ(n)
Abstract
It is known that the Scholz conjecture on addition chains is true for all integers n with ℓ(2n) = ℓ(n) + 1. There exists infinitely many integers with ℓ(2n) ≤ ℓ(n) and we don’t know if the conjecture still holds for them. The conjecture is also proven to hold for integers n with v(n) ≤ 5 and for infinitely many integers with v(n) = 6. There is no specific results on integers with v(n) = 7. In [14], an infinite list of integers satisfying ℓ(n) = ℓ(2n) and v(n) = 7 is given by Thurber. In this paper, we prove that the conjecture holds for all of them.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- addition chainsfast exponentiation
- Contact author(s)
- amadou7 tall @ ucad edu sn
- History
- 2023-01-09: approved
- 2023-01-05: received
- See all versions
- Short URL
- https://ia.cr/2023/020
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2023/020,
author = {Amadou TALL},
title = {The Scholz conjecture on addition chain is true for infinitely many integers with ℓ(2n) = ℓ(n)},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/020},
year = {2023},
url = {https://eprint.iacr.org/2023/020}
}
