Secure and linear cryptosystems using error-correcting codes

A public-key cryptosystem, digital signature and authentication procedures based on a Gallager-type parity-check error-correcting code are presented. The complexity of the encryption and the decryption processes scale linearly with the size of the plaintext Alice sends to Bob. The public-key is pre-corrupted by Bob, whereas a private-noise added by Alice to a given fraction of the ciphertext of each encrypted plaintext serves to increase the secure channel and is the cornerstone for digital signatures and authentication. Various scenarios are discussed including the possible actions of the opponent Oscar as an eavesdropper or as a disruptor

Dynamics of Interacting Neural Networks

The dynamics of interacting perceptrons is solved analytically. For a directed flow of information the system runs into a state which has a higher symmetry than the topology of the model. A symmetry breaking phase transition is found with increasing learning rate. In addition it is shown that a system of interacting perceptrons which is trained on the history of its minority decisions develops a good strategy for the problem of adaptive competition known as the Bar Problem or Minority Game.Comment: 9 pages, 3 figures; typos corrected, content reorganize

Secure exchange of information by synchronization of neural networks

A connection between the theory of neural networks and cryptography is presented. A new phenomenon, namely synchronization of neural networks is leading to a new method of exchange of secret messages. Numerical simulations show that two artificial networks being trained by Hebbian learning rule on their mutual outputs develop an antiparallel state of their synaptic weights. The synchronized weights are used to construct an ephemeral key exchange protocol for a secure transmission of secret data. It is shown that an opponent who knows the protocol and all details of any transmission of the data has no chance to decrypt the secret message, since tracking the weights is a hard problem compared to synchronization. The complexity of the generation of the secure channel is linear with the size of the network.Comment: 11 pages, 5 figure

Public channel cryptography by synchronization of neural networks and chaotic maps

Two different kinds of synchronization have been applied to cryptography: Synchronization of chaotic maps by one common external signal and synchronization of neural networks by mutual learning. By combining these two mechanisms, where the external signal to the chaotic maps is synchronized by the nets, we construct a hybrid network which allows a secure generation of secret encryption keys over a public channel. The security with respect to attacks, recently proposed by Shamir et al, is increased by chaotic synchronization.Comment: 4 page

Statistical mechanical aspects of joint source-channel coding

An MN-Gallager Code over Galois fields, $q$, based on the Dynamical Block Posterior probabilities (DBP) for messages with a given set of autocorrelations is presented with the following main results: (a) for a binary symmetric channel the threshold, $f_c$, is extrapolated for infinite messages using the scaling relation for the median convergence time, $t_{med} \propto 1/(f_c-f)$; (b) a degradation in the threshold is observed as the correlations are enhanced; (c) for a given set of autocorrelations the performance is enhanced as $q$ is increased; (d) the efficiency of the DBP joint source-channel coding is slightly better than the standard gzip compression method; (e) for a given entropy, the performance of the DBP algorithm is a function of the decay of the correlation function over large distances.Comment: 6 page

Cryptography based on neural networks - analytical results

Mutual learning process between two parity feed-forward networks with discrete and continuous weights is studied analytically, and we find that the number of steps required to achieve full synchronization between the two networks in the case of discrete weights is finite. The synchronization process is shown to be non-self-averaging and the analytical solution is based on random auxiliary variables. The learning time of an attacker that is trying to imitate one of the networks is examined analytically and is found to be much longer than the synchronization time. Analytical results are found to be in agreement with simulations

Multi-Choice Minority Game

The generalization of the problem of adaptive competition, known as the minority game, to the case of $K$ possible choices for each player is addressed, and applied to a system of interacting perceptrons with input and output units of the type of $K$-states Potts-spins. An optimal solution of this minority game as well as the dynamic evolution of the adaptive strategies of the players are solved analytically for a general $K$ and compared with numerical simulations.Comment: 5 pages, 2 figures, reorganized and clarifie