Paper 2023/020

The Scholz conjecture on addition chain is true for infinitely many integers with ℓ(2n) = ℓ(n)

Amadou TALL, Université Cheikh Anta Diop de Dakar
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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2023/020}},
      url = {https://eprint.iacr.org/2023/020}
}
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