Chris Monico
In this short note, we give an elementary proof of a universal approximation theorem for neural networks with three hidden layers and increasing, continuous, bounded activation function. The result is weaker than the best known results, but the proof is elementary in the sense that no machinery beyond undergraduate analysis is used.
Chris Monico
Recently, several cryptosystems have been proposed based semidirect products of various algebraic structures. Efficient attacks against several of them have already been given, along with a very general attack. The purpose of this note is to provide an observation that can be used as a point-of-attack for similar systems, and show how it can be used to efficiently cryptanalyze the MOBS system.
Chris Monico, Ayan Mahalanobis
In a recent paper [arXiv:2009.00716], Rahman and Shpilrain proposed a new key-exchange protocol MAKE based on external semidirect product of groups. The purpose of this paper is to show that the key exchange protocol is insecure. We were able to break their challenge problem in under a second.
Dylan Rudy, Chris Monico
We consider a key-exchange protocol based on matrices over a tropical semiring which was recently proposed in \cite{grig19}. We show that a particular private parameter of that protocol can be recovered with a simple binary search, rendering it insecure.