29 research outputs found
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
Training a perceptron by a bit sequence: Storage capacity
A perceptron is trained by a random bit sequence. In comparison to the
corresponding classification problem, the storage capacity decreases to
alpha_c=1.70\pm 0.02 due to correlations between input and output bits. The
numerical results are supported by a signal to noise analysis of Hebbian
weights.Comment: LaTeX, 13 pages incl. 4 figures and 1 tabl
Synchronization of unidirectional time delay chaotic networks and the greatest common divisor
We present the interplay between synchronization of unidirectional coupled
chaotic nodes with heterogeneous delays and the greatest common divisor (GCD)
of loops composing the oriented graph. In the weak chaos region and for GCD=1
the network is in chaotic zero-lag synchronization, whereas for GCD=m>1
synchronization of m-sublattices emerges. Complete synchronization can be
achieved when all chaotic nodes are influenced by an identical set of delays
and in particular for the limiting case of homogeneous delays. Results are
supported by simulations of chaotic systems, self-consistent and mixing
arguments, as well as analytical solutions of Bernoulli maps.Comment: 7 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
Genetic attack on neural cryptography
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.Comment: 8 pages, 12 figures; section 5 amended, typos correcte
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
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
Mutual learning in a tree parity machine and its application to cryptography
Mutual learning of a pair of tree parity machines with continuous and
discrete weight vectors is studied analytically. The analysis is based on a
mapping procedure that maps the mutual learning in tree parity machines onto
mutual learning in noisy perceptrons. The stationary solution of the mutual
learning in the case of continuous tree parity machines depends on the learning
rate where a phase transition from partial to full synchronization is observed.
In the discrete case the learning process is based on a finite increment and a
full synchronized state is achieved in a finite number of steps. The
synchronization of discrete parity machines is introduced in order to construct
an ephemeral key-exchange protocol. The dynamic learning of a third tree parity
machine (an attacker) that tries to imitate one of the two machines while the
two still update their weight vectors is also analyzed. In particular, the
synchronization times of the naive attacker and the flipping attacker recently
introduced in [1] are analyzed. All analytical results are found to be in good
agreement with simulation results