Wyniki wyszukiwania - BazTech

1

Distance of the initial weights of tree parity machine drawn from different distributions

Dolecki M., Kozera R.

Advances in Science and Technology. Research Journal

|

2015

|

Vol. 9, nr 26

137–-142

EN

It is well-known that artificial neural networks have the ability to learn based on the provisions of new data. A special case of the so-called supervised learning is a mutual learning of two neural networks. This type of learning applied to a specific networks called Tree Parity Machines (abbreviated as TPM networks) leads to achieving consistent weight vectors in both of them. Such phenomenon is called a network synchronization and can be exploited while constructing cryptographic key exchange protocol. At the beginning of the learning process both networks have initialized weights values as random. The time needed to synchronize both networks depends on their initial weights values and the input vectors which are also randomly generated at each step of learning. In this paper the relationship between the distribution, from which the initial weights of the network are drawn, and their compatibility is discussed. In order to measure the initial compatibility of the weights, the modified Euclidean metric is invoked here. Such a tool permits to determine the compatibility of the network weights’ scaling in regard to the size of the network. The proper understanding of the latter permits in turn to compare TPM networks of various sizes. This paper contains the results of the simulation and their discussion in the context of the above mentioned issue.

2

The evaluation of the TPM synchronization on the basis of their outputs

Dolecki M., Kozera R., Lenik K.

Journal of Achievements in Materials and Manufacturing Engineering

|

2013

|

Vol. 57, nr 2

91--98

EN

Purpose: Tree Parity Machines are specific artificial neural networks used to construct relatively secure key exchange protocol [12,15,24]. The level of networks’ compatibility is measured by weight vectors mutual overlap. However, to calculate such mutual overlap, one needs to be familiar with both weights’ vectors, which is impossible in practical key exchange. This paper discusses other schemes to evaluate compatibility of weights’ vectors. The first one uses Euclidean distance of both weights’ vectors. The second one is based on frequencies of common TPM’s outputs and as such does not rely on the weights’ vectors. Both approaches to handle secure key exchange protocol facilitate more extended analysis of many technical processes in which a vital role plays an incorporation of a non-standard high-quality method securing any sensitive data. Design/methodology/approach: Computer simulations of TPM synchronization are conducted using authors’ program and the obtained results are statistically analyzed herein. Findings: We found experimentally that mutual overlap of the weights’ vectors is highly correlated with Euclidean distance. Additionally, frequencies of common outputs in given numbers of learning cycles stay in high correlation with this mutual overlap and Euclidean distance. The latter can subsequently be used to draw pertinent conclusions about TPM’s weights compatibility. Practical implications: Proposed methods, especially frequencies analysis, can be applied to key exchange protocol to improve its security. Determining the vectors compatibility level before synchronization completion allows qualifying this synchronization to one of the possible time classes. Originality/value: New ideas presented in this work involve application of Euclidean distance and common output frequencies to calculate the networks compatibility given by weights mutual overlap.

3

Distribution of the tree parity machine synchronization time

Dolecki M., Kozera R.

Advances in Science and Technology. Research Journal

|

2013

|

Vol. 7, nr 18

20--27

EN

Neural networks’ synchronization by mutual learning discovered and described by Kanter et al. [12] can be used to construct relatively secure cryptographic key exchange protocol in the open channel. This phenomenon based on simple mathematical operations, can be performed fast on a computer. The latter makes it competitive to the currently used cryptographic algorithms. An additional advantage is the easiness in system scaling by adjusting neutral network’s topology, what results in satisfactory level of security [24] despite different attack attempts [12, 15]. With the aid of previous experiments, it turns out that the above synchronization procedure is a stochastic process. Though the time needed to achieve compatible weights vectors in both partner networks depends on their topology, the histograms generated herein render similar distribution patterns. In this paper the simulations and the analysis of synchronizations’ time are performed to test whether these histograms comply with histograms of a particular well-known statistical distribution. As verified in this work, indeed they coincide with Poisson distribution. The corresponding parameters of the empirically established Poisson distribution are also estimated in this work. Evidently the calculation of such parameters permits to assess the probability of achieving both networks’ synchronization in a given time only upon resorting to the generated distribution tables. Thus, there is no necessity of redoing again time-consuming computer simulations.