Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Triangular polynomial maps in characteristic $p$   This paper came to existence out of the desire to understand iterations of
strictly triangular polynomial maps over finite fields. This resulted in two
connected results:
  First, we give a generalization of $\F_p$-actions on $\F_p^n$ and their
description by "locally iterative higher derivations", namely $\Z$-actions on
$\F_p^n$ and show how to describe them by what we call "$\Z$-flows". We prove
equivalence between locally finite polynomial automorphisms (LFPEs) over finite
fields and $\Z$-flows over finite fields. We elaborate on $\Z$-flows of
strictly triangular polynomial maps.
  Second, we describe how one can efficiently evaluate iterations of triangular
polynomial permutations on $\F_p^n$ which have only one orbit. We do this by
determining the equivalence classes in the triangular permutation group of such
elements. We show how to conjugate them all to the map $z\lp z+1$ on the ring
$\Z/p^n\Z$ (which is identified with $\F_{p^n}$), making iterations trivial. An
application in the form of fast-forward functions from cryptography is given.

24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat