Neural Networks Meet Elliptic Curve Cryptography: A Novel Approach to Secure Communication

TL;DR

This work investigates neural cryptography by embedding elliptic-curve public-key cryptography into a neural framework to secure communication between Alice and Bob against Eve. It employs a three-network, adversarial, GAN-like setup where Bob generates a public/private key pair $K_{PUBLIC}$ and $K_{PRIVATE}$, Alice encrypts with $K_{PUBLIC}$, and Eve attempts unauthorized decryption. Across five elliptic curves, the system achieves high decryption accuracy for Bob and near-random performance for Eve under standard training, but Eve's accuracy increases to about $61$–$65\%$ when trained twice per batch, exposing a security vulnerability and motivating CPA-style defenses. The findings highlight the potential of neural ECC-based cryptography for secure communications while underscoring the need for stronger resilience against adaptive eavesdropping.

Abstract

In recent years, neural networks have been used to implement symmetric cryptographic functions for secure communications. Extending this domain, the proposed approach explores the application of asymmetric cryptography within a neural network framework to safeguard the exchange between two communicating entities, i.e., Alice and Bob, from an adversarial eavesdropper, i.e., Eve. It employs a set of five distinct cryptographic keys to examine the efficacy and robustness of communication security against eavesdropping attempts using the principles of elliptic curve cryptography. The experimental setup reveals that Alice and Bob achieve secure communication with negligible variation in security effectiveness across different curves. It is also designed to evaluate cryptographic resilience. Specifically, the loss metrics for Bob oscillate between 0 and 1 during encryption-decryption processes, indicating successful message comprehension post-encryption by Alice. The potential vulnerability with a decryption accuracy exceeds 60\%, where Eve experiences enhanced adversarial training, receiving twice the training iterations per batch compared to Alice and Bob.

Figures (6)

• Figure 1: Asymmetric cryptosystem.
• Figure 2: Encryption process flow, illustrating how Alice encrypts a plaintext message using Bob's public key.
• Figure 3: Overview of the system, the interaction between Alice, Bob, and Eve.
• Figure 4: Training flow of the neural networks.
• Figure 5: Loss functions for the ABE model, Bob and Eve, with different curves.