A representation of the $p$-sylow subgroup of $\perm(\F_p^n)$ and  a cryptographic application

Stefan Maubach

Paper 2011/383

A representation of the $p$-sylow subgroup of $\perm(\F_p^n)$ and a cryptographic application

Stefan Maubach

Abstract

This article concerns itself with the triangular permutation group, induced by triangular polynomial maps over $\F_p$, which is a $p$-sylow subgroup of $\perm(\F_p^n)$. The aim of this article is twofold: on the one hand, we give an alternative to $\F_p$-actions on $\F_p^n$, namely $\Z$-actions on $\F_p^n$ and how to describe them as what we call ``$\Z$-flows''. On the other hand, we describe how the triangular permutation group can be used in applications, in particular we give a cryptographic application for session-key generation. The described system has a certain degree of information theoretic security. We compute its efficiency and storage size. To make this work, we give explicit criteria for a triangular permutation map to have only one orbit, which we call ``maximal orbit maps''. We describe the conjugacy classes of maximal orbit maps, and show how one can conjugate them even further to the map $z\lp z+1$ on $\Z/p^n\Z$.

Note: 21 pages

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published elsewhere. Unknown where it was published
Keywords: Diffie-Hellmann session key exchange
Contact author(s): stefan maubach @ gmail com
History: 2011-07-15: received
Short URL: https://ia.cr/2011/383
License: CC BY

BibTeX

@misc{cryptoeprint:2011/383,
      author = {Stefan Maubach},
      title = {A representation of the $p$-sylow subgroup of $\perm(\F_p^n)$ and  a cryptographic application},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/383},
      year = {2011},
      url = {https://eprint.iacr.org/2011/383}
}