A secure key-exchange protocol with an absence of injective functions

TL;DR

This paper presents a neural cryptography key-exchange protocol that enhances security by increasing synchronization time and decreasing attacker success probability without relying on traditional number theory or trapdoor functions.

Contribution

The authors introduce a neural cryptography protocol that achieves security through network synchronization properties, eliminating the need for injective functions or trapdoor mechanisms.

Findings

Synchronization time scales with L^2

Attacker success probability decreases exponentially with L

Protocol offers a secure alternative to traditional cryptography

Abstract

The security of neural cryptography is investigated. A key-exchange protocol over a public channel is studied where the parties exchanging secret messages use multilayer neural networks which are trained by their mutual output bits and synchronize to a time dependent secret key. The weights of the networks have integer values between $\pm L$. Recently an algorithm for an eavesdropper which could break the key was introduced by Shamir et al. [adi]. We show that the synchronization time increases with $L^2$ while the probability to find a successful attacker decreases exponentially with $L$. Hence for large $L$ we find a secure key-exchange protocol which depends neither on number theory nor on injective trapdoor functions used in conventional cryptography.