Statistical description of output states of the neural network "biometrics-code" transformers

The article considers a problem of statistical description of the neural network "biometrics- code" transformer. It is shown that the classic binominal law of distribution is applicable only for ideal "biometrics- code" transformers. According to the standard ΓOCT P 52633.0-2006 stipulating general requirements for output codes, the ideal "biometrics-code" transformers should provide absolute dual independence of output code bits. For real "biometrics-code" transformers it is necessary to modify the binary law of distribution to take into consideration the misbalance of probabilities of biometric code bits' states and the correlation of the bits. Any misbalance of "0" and "1" states of emergence probability will inevitably result in quality decrease of "biometrics-code" transformers (decrease in output codes entropy). The article also considers registration of existing correlations between biometric code bits. During statistical analysis the authors have imitated the operation of a "biometrics-code" transformer with 256 outputs. The identical value of dual coefficients of correlation between output code bits has been taken as the only controlled parameter - "r". The article adduces the distribution of Hamming distance values' emergence probabilities with different values of the controlled parameter r = 0:05; 0:10; : : : ; 0:48. Another peculiarity of real "biometrics-code" transformer is that the values of dual coefficients of correlation between code bits have a symmetric distribution relative to the point r = 0:0. The article gives an example of correlation coefficients distribution in the 256-bit "biometrics-code" transformer. The most probable value of correlation coefficients is zero; all the obtained values of correlation coefficients remain in the range ±0:5. Simple averaging of correlation coefficients is inadmissible. According to the experience, the best approach to obtain a good match of imitation results with reality is to use mathematical expectation of modules of dual correlation coefficients as the controlled parameter - r. In case of averaged parameters application the dimensionality of statistical description of output code states may significantly decrease. If the key length is n = 256, the statistical description in the Hamming distances dimension is displayed in the form of corresponding tables with convertible parameters r (pitch 0.01, interval from 0.00 to 0.99) and P ("0") (pitch 0.01, interval from 0.01 to 0.5).