Finite field models of Raleigh-Akiyama polynomials for Hecke groups

Following work of Raleigh and Akiyama (\cite{raleigh1962fourier, akiyama1992note}), in \cite{interpolating} we considered (among other objects) families of weight zero meromorphic modular forms $J_m$ for Hecke groups $G(\lambda_m)$. We conjectured in \cite{interpolating} that, for a certain uniformizing variable $X_m$, the $J_m$ have Fourier expansions $J_m = 1/X_m + \sum_{n = 0}^{\infty} A_n(m) X_m^n$, where the $A_n(x)$ are polynomials in $\mathbb{Q}[x]$. The present article is concerned with models $\mathcal{A}_n[p](x)$ of the $A_n(x)$: polynomials representing self-maps of finite fields with characteristic $p$. The main content is a conjecture specifying $\mathcal{A}_n[p](x)$ up to a multiplicative constant for certain families of $n$ and $p$, based on numerical experiments.Comment: Accepted for publication in the journal "Integers

Unsupervised Time Series Extraction from Controller Area Network Payloads

This paper introduces a method for unsupervised tokenization of Controller Area Network (CAN) data payloads using bit level transition analysis and a greedy grouping strategy. The primary goal of this proposal is to extract individual time series which have been concatenated together before transmission onto a vehicle's CAN bus. This process is necessary because the documentation for how to properly extract data from a network may not always be available; passenger vehicle CAN configurations are protected as trade secrets. At least one major manufacturer has also been found to deliberately misconfigure their documented extraction methods. Thus, this proposal serves as a critical enabler for robust third-party security auditing and intrusion detection systems which do not rely on manufacturers sharing confidential information.Comment: 2018 IEEE 88th Vehicular Technology Conference (VTC2018-Fall