The Battery-Discharge-Model: A Class of Stochastic Finite Automata to Simulate Multidimensional Continued Fraction Expansion

TL;DR

This paper introduces the Battery-Discharge-Model, a stochastic automaton that accurately simulates the complexity measures of multidimensional continued fraction expansions, aiding cryptanalysis of stream ciphers.

Contribution

It defines an infinite stochastic automaton and provides finite approximations with polynomially many states for analyzing complexity in cryptographic sequences.

Findings

Finite approximations achieve exponentially small error

Polynomially many states suffice for accurate simulation

Model effectively captures complexity behavior in cryptanalysis

Abstract

We define an infinite stochastic state machine, the Battery-Discharge-Model (BDM), which simulates the behaviour of linear and jump complexity of the continued fraction expansion of multidimensional formal power series, a relevant security measure in the cryptanalysis of stream ciphers. We also obtain finite approximations to the infinite BDM, where polynomially many states suffice to approximate with an exponentially small error the probabilities and averages for linear and jump complexity of M-multisequences of length n over the finite field F_q, for any M, n, q.