On the Number of Linear Finite Transducers

Abstract

The notion of linear finite transducer (LFT) plays a crucial role in some cryptographic systems. However, as far as we know, no study was ever conducted to count and enumerate these transducers, which is essential to verify if the size of the key space, of the aforementioned systems, is large enough to prevent an exhaustive search attack. In this work we present a way to estimate the number and percentage of injective equivalence classes by introducing a canonical form for LFTs and a procedure to test LFTs equivalence.