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**2011/383**

**Title:**

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

**Authors:**
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 mapsâ€™'. 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.

**ePrint:**
https://eprint.iacr.org/2011/383

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