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Consider the following sequence as an example:.

we can see that the procedure is equivalent to starting with a good estimate of the integral IC and doing the simulation on the difference between the functions. If C(x) is a good approximation, the correction term should be small. The open triangles in Figure 17.8 show the results of using control variates to improve convergence of the integral with the factor set to unity. The calculations were done the same way as for importance sampling. The gure shows that the variance reduction in this case is even more effective than it was with importance sampling. A further advantage of the control variate approach in this case is that the importance function approach requires that the random variables conform to a cubic probability distribution function, which involves nding the inverse of a quartic function, while the control variable is a simple cubic function that is not inverted. Thus, the programming and computational efforts are both reduced. The control variate does not have to match the function to be integrated exactly. A more general statement of control variate theory is that, if Y is an estimator to be evaluated by simulation, then the modi ed simulation is governed by Z = Y (C C ) The optimum value of is = Cov (Y , C) Var(C) (17.57) (17.56)

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0040343B 0040343E 00403440 00403443 00403446 00403448 0040344B 0040344E 00403451 00403454 8B45 8B00 3345 8B4D 8901 8B45 8945 8B45 3345 8945 CC D8 CC D4 D8 DC D4 DC MOV MOV XOR MOV MOV MOV MOV MOV XOR MOV EAX,[EBP-34] EAX,[EAX] EAX,[EBP-28] ECX,[EBP-34] [ECX],EAX EAX,[EBP-2C] [EBP-28],EAX EAX,[EBP-24] EAX,[EBP-2C] [EBP-24],EAX

One almost trivial method that would make it a bit more difficult to identify this sequence would consist of simply randomizing the use of registers in the code. The code sequence uses registers separately at several different phases.

2 Var(Z) = Var(Y )[1 Y ,C ]

20

Consider, for example, the instructions at 00403448 and 0040344E. Both instructions load a value into EAX, which is used in instructions that follow. It would be quite easy to modify these instructions so that the first uses one register and the second uses another register. It is even quite easy to change the base stack frame pointer (EBP) to use another general-purpose register. Of course, you could change way more than just registers (see the following section on metamorphism), but by restricting the magnitude of the modification to something like register usage you re enabling the creation of fairly trivial routines that would simply know in advance which bytes should be modified in order to alter register usage it would all be hard-coded, and the specific registers would be selected randomly at runtime.

(17.58)

0040343B 0040343E 00403440 00403443 00403446 00403448 0040344B 0040344E 00403451 00403454 8B57 8B02 3347 8B5F 8903 8B77 8977 8B4F 334F 894F CC D8 CC D4 D8 DC D4 DC MOV MOV XOR MOV MOV MOV MOV MOV XOR MOV EDX,[EDI-34] EAX,[EDX] EAX,[EDI-28] EBX,[EDI-34] [EBX],EAX ESI,[EDI-2C] [EDI-28],ESI ECX,[EDI-24] ECX,[EDI-2C] [EDI-24],ECX

This code provides an equivalent-functionality alternative to the original sequence. The emphasized bytecodes represent the bytecodes that have changed from the original representation. To simplify the implementation of such transformation, it is feasible to simply store a list of predefined bytes that could be altered and in what way they can be altered. The program could then randomly fiddle with the available combinations during the self-replication process and generate a unique machine code sequence. Because this kind of implementation requires the creation of a table of hard-coded information regarding the specific code bytes that can be altered, this approach would only be feasible when most of the program is encrypted or encoded in some way, as described earlier. It would not be practical to manually scramble an entire program in this fashion. Additionally, it goes without saying that all registers must be saved and restored before entering a function that can be polymorphed in this fashion.

In other words, the requirement is that the control variate be well correlated with the uncontrolled estimator.

Because polymorphism is limited to very superficial modifications on the malware s decryption code, there are still plenty of ways for antivirus programs to identify polymorphed code by analyzing the code and extracting certain highlevel information from it.

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