基于同余方程和改进的压扁控制流的混淆算法

针对现有控制流混淆算法的混淆结果单一的问题，提出了一种基于同余方程和改进的压扁控制流混淆算法。首先，使用密钥和一组同余方程来生成源代码的基本块中需要使用的不透明谓词；其次，基于Logistic混沌映射提出了一种新的N态不透明谓词构造算法，并将其应用到现有的压扁控制流算法中，对现有的压扁控制流算法进行改进；最后，将上述两个对源码进行混淆的算法结合，以此来增加源代码中控制流的复杂度，使其更难被破解。与现有的基于混沌不透明谓词的压扁控制流算法相比，所提混淆算法使混淆后代码的防篡改攻击时间平均提高了22%以上，总圈复杂度平均提高了34%以上。实验结果表明，所提算法能够保证混淆后程序执行结果的正确性并且具有很高的圈复杂度，能够有效地抵抗静态攻击和动态攻击。

Obfuscating algorithm based on congruence equation and improved flat control flow

Aiming at the simple obfuscating result of the existing control flow obfuscating algorithm, an obfuscating algorithm based on congruence equation and improved flat control flow was presented. First of all, a kind of opaque predicate used in the basic block of the source code was created by using secret keys and a group of congruence equation. Then, a new algorithm for creating N-state opaque predicate was presented based on Logistic chaotic mapping. The proposed algorithm was applied to the existing flat control flow algorithm for improving it. Finally, according to the combination of the above two proposed algorithms for obfuscating the source code, the complexity of the flat control flow in the code was increased and make it more difficult to be cracked. Compared with the flat control flow algorithm based on chaotic opaque predicate, the code's tamper-proof attack time of the obfuscated code was increased by above 22% on average and its code's total cyclomatic complexity was improved by above 34% on average by using the proposed obfuscating algorithm. The experimental results show that, the proposed algorithm can guarantee the correctness of execution result of the obfuscated program and has a high cyclomatic complexity, so it can effectively resist static and dynamic attacks.