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to filter the run traces—leaving only instructions executed by the “Password” module.

To analyze the effectiveness of the ordering (control flow) obfuscation, statistics

on the differences between three different run traces were gathered using a modification

of Levenshtein Distance (LD), a generalization of Hamming Distance, to compute the

edit-distance—the number of assembly instruction insertions, deletions, or substitutions

needed to transform one trace into the other; we've modified LD to consider each

instruction instead of each character in the run traces. Fig. 7.4 illustrates the significant

differences that exist between the traces at the point of the obfuscated trial limitation

check. The randomized control-flow obfuscation causes significant differences in

subsequent executions of the trial limitation check—hopefully creating enough of a

deterrent for a reverse engineer by hampering live and static analysis efforts. Table 7.9

contains the statistical data that was gathered for the analysis.

A C++ implementation of Levenshtein Distance, written for this solution, can be

downloaded from http://reversingproject.info/repository.php?fileID=7_6_1. Note that

computing the edit-distance between two large files of any type can take many hours a

modern PC. For reference, the average size of three traces analyzed in this section is

10MB, and to compute the edit-distance between two of them required an average of ~20

hours of CPU time on an Intel Pentium 1.6GHz Dual-core processor. The LD

implementation employed in this analysis uses a dynamic-programming approach that

requires O(m) space; note that some reference implementations of LD require O(mn)

space since they use a (m + 1) x (n + 1) matrix which is impractical for large files [25].

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