Statistical Study On The Number Of Injective Linear Finite Transducers

TL;DR

This paper estimates the number of non-equivalent injective linear finite transducers using random sampling and recurrence relations, aiding cryptographic system analysis.

Contribution

It introduces a method to approximate the count of injective LFTs and estimates their percentage, advancing understanding of their key space.

Findings

Approximate count of non-equivalent injective LFTs

Recurrence relation for canonical LFTs

Estimated percentage of τ-injective LFTs

Abstract

The notion of linear finite transducer (LFT) plays a crucial role in some cryptographic systems. In this paper we present a way to get an approximate value, by random sampling, for the number of non-equivalent injective LFTs. By introducing a recurrence relation to count canonical LFTs, we show how to estimate the percentage of $\tau$-injective LFTs. Several experimental results are presented, which by themselves constitute an important step towards the evaluation of the key space of those systems.