Asymmetric Neural Cryptography with Homomorphic and Probabilistic Properties

Abstract

Recent integrations of artificial intelligence in cryptography have improved traditional methods and known crypto attacks. However, the potential of combining neural cryptography with homomorphic and probabilistic encryption remains underexplored. This study introduces a new system that establishes secure communication between two neural networks using asymmetric, homomorphic, and probabilistic encryption across five neural networks. These include an encryption network, a decryption network, an eavesdropping network, and two networks implementing addition and multiplication through the Neural Accumulator and Neural Arithmetic Logic Unit models. The results are created using different elliptic curves and dropout rates to measure the variability in the ciphertext among the curves and rates. The results show that the system can generate random ciphertexts and that the decryption network can almost perfectly decrypt directly encrypted messages with a decryption accuracy of approximately 100%. For messages processed by the homomorphic networks, the decryption accuracy of addition is nearly 100%, while for multiplication, the accuracy varies between approximately 91% and 98%. A drop in the decryption accuracy is observed for both operations in one of the dropout rate and curve combinations. Further work should focus on reducing ciphertext value variability and enhancing consistency. Additionally, integrating a more robust adversarial model is crucial for increasing the system's security, and the homomorphic networks could be replaced with functions for addition and multiplication. The current setup is somewhat homomorphic, but it should be considered for further work to be expanded to be fully homomorphic.