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Affine equivalence classification of Boolean functions has significant applications in logic synthesis and cryptography. Previous studies for classification have been limited by the large set of Boolean functions and the complex operations on the affine group. Although there are many research on affine equivalence classification for parts of Boolean functions in recent years, there are very few results for the entire set of Boolean functions. The best existing result has been achieved by Harrison with 15768919 affine equivalence classes for 6-variable Boolean functions. This paper presents a concise formula for affine equivalence classification of the entire set of Boolean functions as well as a formula for affine classification of Boolean functions with distinct ON-set size respectively. The method outlined in this paper greatly simplifies the affine group's action by constructing an isomorphism mapping from the affine group to a permutation group. By this method, we can compute the affine equivalence classes for up to 10 variables. Experiment results indicate that our scheme for calculating the affine equivalence classes for more than 6 variables is a significant advancement over previous published methods. [ABSTRACT FROM PUBLISHER]

In recent years, malware with strong concealment uses encrypted protocol to evade detection. Thus, encrypted traffic identification can help security analysts to be more effective in narrowing down those encrypted network traffic. Existing methods are protocol independent, such as statistical-based and machine-learning-based approaches. Statistical-based approaches, however, are confined to payload length and machine-learning-based approaches have a low recognition rate for encrypted traffic using undisclosed protocols. In this paper, we proposed a heuristic statistical testing (HST) approach that combines both statistics and machine learning and has been proved to alleviate their respective deficiencies. We manually selected four randomness tests to extract small payload features for machine learning to improve real-time performances. We also proposed a simple handshake skipping method called HST-R to increase the classification accuracy. We compared our approach with other identification approaches on a testing dataset consisting of traffic that uses two known, two undisclosed, and one custom cryptographic protocols. Experimental results showed that HST-R performs better than other traditional coding-based, entropy-based, and ML-based approaches. We also showed that our handshake skipping method could generalize better for unknown cryptographic protocols. Finally, we also conducted experimental comparisons among different classification algorithms. The results showed that C4.5, with our method, has the highest identification accuracy for secure sockets layer and secure shell traffic. [ABSTRACT FROM AUTHOR]