Cryptography based on neural networks—analytical results

The 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 show nt ob enon-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.

[1]  I Kanter,et al.  Interacting neural networks. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Opper.  Statistical physics estimates for the complexity of feedforward neural networks. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  C. Van Den Broeck,et al.  Clipped-Hebbian Training of the Perceptron , 1993 .

[4]  Douglas R. Stinson,et al.  Cryptography: Theory and Practice , 1995 .

[5]  Wolfgang Kinzel,et al.  Improving a Network Generalization Ability by Selecting Examples , 1990 .

[6]  W. Kinzel,et al.  Secure exchange of information by synchronization of neural networks , 2002 .

[7]  R. Urbanczik,et al.  SELF-AVERAGING AND ON-LINE LEARNING , 1998, cond-mat/9805339.

[8]  M. V. Rossum,et al.  In Neural Computation , 2022 .

[9]  R. Metzler,et al.  Dynamics of interacting neural networks , 1999 .

[10]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[11]  Kanter,et al.  Statistical mechanics of a multilayered neural network. , 1990, Physical review letters.

[12]  N. Caticha,et al.  On-line learning in parity machines , 1996 .

[13]  O. Kinouchi,et al.  Optimal generalization in perceptions , 1992 .

[14]  Christian Van den Broeck,et al.  Statistical Mechanics of Learning , 2001 .