Performance and Statistical Analysis of Stream ciphers in GSM Communications

Abstract

For a stream cipher to be secure, the keystream generated by it should be uniformly random with parameter 1/2. Statistical tests check whether the given sequence follow a certain probability distribution. In this paper, we perform a detailed statistical analysis of various stream ciphers used in GSM 2G, 3G, 4G and 5G communications. The sequences output by these ciphers are checked for randomness using the statistical tests defined by the NIST Test Suite. It should also be not possible to derive any information about secret key and the initial state of the cipher from the keystream. Therefore, additional statistical tests based on properties like Correlation between Keystream and Key, and Correlation between Keystream and IV are also performed. Performance analysis of the ciphers also has been done and the results tabulated. Almost all the ciphers pass the tests in the NIST test suite with 99% confidence level. For A5/3 stream cipher, the correlation between the keystream and key is high and correlation between the keystream and IV is low when compared to other ciphers in the A5 family.

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