Genetic attack on neural cryptography

TL;DR

This paper investigates the security of neural cryptography by analyzing how genetic algorithms can improve attack success rates and how scaling laws affect the complexity of such attacks.

Contribution

It introduces a genetic algorithm-based attack method and analyzes its effectiveness and scaling properties in neural cryptography.

Findings

Genetic algorithms significantly improve attack success probabilities.

Success probability decreases exponentially with increasing synaptic depth.

Scaling laws for attack complexity are consistent across different attack methods.

Abstract

Different scaling properties for the complexity of bidirectional synchronization and unidirectional learning are essential for the security of neural cryptography. Incrementing the synaptic depth of the networks increases the synchronization time only polynomially, but the success of the geometric attack is reduced exponentially and it clearly fails in the limit of infinite synaptic depth. This method is improved by adding a genetic algorithm, which selects the fittest neural networks. The probability of a successful genetic attack is calculated for different model parameters using numerical simulations. The results show that scaling laws observed in the case of other attacks hold for the improved algorithm, too. The number of networks needed for an effective attack grows exponentially with increasing synaptic depth. In addition, finite-size effects caused by Hebbian and anti-Hebbian learning are analyzed. These learning rules converge to the random walk rule if the synaptic depth is small compared to the square root of the system size.