Dynamics of neural cryptography

Synchronization of neural networks has been used for novel public channel protocols in cryptography. In the case of tree parity machines the dynamics of both bidirectional synchronization and unidirectional learning is driven by attractive and repulsive stochastic forces. Thus it can be described well by a random walk model for the overlap between participating neural networks. For that purpose transition probabilities and scaling laws for the step sizes are derived analytically. Both these calculations as well as numerical simulations show that bidirectional interaction leads to full synchronization on average. In contrast, successful learning is only possible by means of fluctuations. Consequently, synchronization is much faster than learning, which is essential for the security of the neural key-exchange protocol. However, this qualitative difference between bidirectional and unidirectional interaction vanishes if tree parity machines with more than three hidden units are used, so that those neural networks are not suitable for neural cryptography. In addition, the effective number of keys which can be generated by the neural key-exchange protocol is calculated using the entropy of the weight distribution. As this quantity increases exponentially with the system size, brute-force attacks on neural cryptography can easily be made unfeasible.Comment: 9 pages, 15 figures; typos correcte

Synchronization of random walks with reflecting boundaries

Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are found to increase proportional to the square of the system size. Additionally, the probability of synchronization in a given step is analyzed, which converges to a geometric distribution for long synchronization times. From this asymptotic behavior the number of steps required to synchronize an ensemble of independent random walk pairs is deduced. Here the synchronization time increases with the logarithm of the ensemble size. The results of this model are compared to those observed in neural synchronization.Comment: 10 pages, 7 figures; introduction changed, typos correcte

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

Successful attack on permutation-parity-machine-based neural cryptography

An algorithm is presented which implements a probabilistic attack on the key-exchange protocol based on permutation parity machines. Instead of imitating the synchronization of the communicating partners, the strategy consists of a Monte Carlo method to sample the space of possible weights during inner rounds and an analytic approach to convey the extracted information from one outer round to the next one. The results show that the protocol under attack fails to synchronize faster than an eavesdropper using this algorithm.Comment: 4 pages, 2 figures; abstract changed, note about chaos cryptography added, typos correcte

Efficient statistical inference for stochastic reaction processes

We address the problem of estimating unknown model parameters and state variables in stochastic reaction processes when only sparse and noisy measurements are available. Using an asymptotic system size expansion for the backward equation we derive an efficient approximation for this problem. We demonstrate the validity of our approach on model systems and generalize our method to the case when some state variables are not observed.Comment: 4 pages, 2 figures, 2 tables; typos corrected, remark about Kalman smoother adde

Transformation of terrestrial organic matter along thermokarst-affected permafrost coasts in the Arctic

The changing climate in the Arctic has a profound impact on permafrost coasts, which are subject to intensified thermokarst formation and erosion. Consequently, terrestrial organic matter (OM) is mobilized and transported into the nearshore zone. Yet, little is known about the fate of mobilized OM before and after entering the ocean. In this study we investigated a retrogressive thaw slump (RTS) on Qikiqtaruk - Herschel Island (Yukon coast, Canada). The RTS was classified into an undisturbed, a disturbed (thermokarst-affected) and a nearshore zone and sampled systematically along transects. Samples were analyzed for total and dissolved organic carbon and nitrogen (TOC, DOC, TN, DN), stable carbon isotopes (δ13C-TOC, δ13C-DOC), and dissolved inorganic nitrogen (DIN), which were compared between the zones. C/N-ratios, δ13C signatures, and ammonium (NH4-N) concentrations were used as indicators for OM degradation along with biomarkers (n-alkanes, n-fatty acids, n-alcohols). Our results show that OM significantly decreases after disturbance with a TOC and DOC loss of 77 and 55% and a TN and DN loss of 53 and 48%, respectively. C/N-ratios decrease significantly, whereas NH4-N concentrations slightly increase in freshly thawed material. In the nearshore zone, OM contents are comparable to the disturbed zone. We suggest that the strong decrease in OM is caused by initial dilution with melted massive ice and immediate offshore transport via the thaw stream. In the mudpool and thaw stream, OM is subject to degradation, whereas in the slump floor the nitrogen decrease is caused by recolonizing vegetation. Within the nearshore zone of the ocean, heavier portions of OM are directly buried in marine sediments close to shore. We conclude that RTS have profound impacts on coastal environments in the Arctic. They mobilize nutrients from permafrost, substantially decrease OM contents and provide fresh water and nutrients at a point source