Abstract
The paper deals with the problem of determination of error probability of cryptography and safety codes used within the safety-related railway applications with increasing safety integrity level (SIL). In the paper are also described requirements for cryptographic block code and safety linear block code in safety-related communications for railway application. The main part is oriented to the description of mathematical apparatus for the error probability of the cryptography and safety block codes for communication between two safety-related devices across GSM-R communication channel. The practical results are related to the quantitative evaluation of an average error probability of the cryptography and safety codes for several lengths of safety-related messages which are expanded about determination of the cryptography degradation with using GMSK modulation scheme.
Highlights
With respect to high requirement to Safety Integrity Level (SIL) of an interlocking and a communication system, the safety of subsystems cannot be demonstrated only by tests and by theoretical models based on quantitative analysis
Concerning to the application of safety codes within safety-related communication system the linear block detection codes are recommended with the decoding principle based on syndrome technique of determination
They considered the recommendations for the safety analysis of the encrypted transmission affected with noise environment of GSM-R with GMSK modulation, which has become a prospective medium for transmitting messages in the developing ETCS system
Summary
With respect to high requirement to Safety Integrity Level (SIL) of an interlocking and a communication system, the safety of subsystems cannot be demonstrated only by tests and by theoretical models based on quantitative analysis. 3. Mathematical Apparatus for Error Probability Determination of Cryptographic and Safety Codes transmission system which consists of transmission encoder/decoder and GSM-R communication channel. According to the recommendation from the standard for communications in the railway applications [4] for determination of the cryptographic decoder error probability is necessary to consider the set of block cryptography encoder with the private key where the safety-related message of length n bits is divided into the words with the length of k bits and after that encrypted with the agreed algorithm. If we assume independence of the blocks with errors on the input of the cryptographic decoder the error probability of encrypted word Pcw depends on the communication channel bit error rate Pb and is defined as: Pcw = P (w|be) 1 − (1 − Pb)n ,. By substitution (14) into (13) for Eb1/Eb and by using the result from (9) we obtain: ln g(n, k)
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