Obfuscation of Abstract Data-Types - Rowan

CHAPTER 2. OBFUSCATIONS FOR INTERMEDIATE LANGUAGE 37
M
ThenEdge
ElseEdge
ThenVert
Es
ElseVert
Es
Figure 2.8: Flow graph to build a conditional expression
Next, we create a test C corresponding to i %2 == 0 in the the predicate
is even(I,C) and we create an expression J for the indices of the new arrays,
using the predicate index(I,J) (we omit the details of these predicates).
Now, we need to create vertices corresponding to the branches of the conditional
— the flow graph we want to create is shown in Figure 2.8. To create
the “then” branch, we first obtain a fresh label ThenLab with which we create
a new vertex ThenVert. This vertex needs to contain an instruction B 1 [J] = V
and have the same outgoing edges as N . Then we create a new incoming edge,
ThenEdge, for ThenVert. The construction of the “else” branch is similar (we
build the instruction B 2 [J] = V instead).
Finally, we are ready to build a new vertex M which replaces N . This vertex
contains an instruction for the conditional which has label L. The outgoing edges
for this vertex are ThenEdge and ElseEdge.
Replacing uses of the original array is slightly easier. Instead of manually
building ThenVert and ElseVert we can use the predicate subst to replace A[I]
with B 1 [J] or B 2 [J] as appropriate.
We can adapt this specification for other array splits. In Section 1.3.6, we
defined an array split in terms of three functions ch, f 1 and f 2 . The predicate
is even corresponds to the function ch and index corresponds to f 1 and f 2
(which are equal for our example). So by defining a predicate that represents
ch and two predicates for f 1 and f 2 , we can write a specification for any split
that creates two new arrays.
2.3.8 Creating an irreducible flow graph
In Section 2.2.2, we saw how by placing an if statement before a loop we could
create a method with an irreducible control flow graph. Could we specify this
transformation in PLP? The control flow graph that we want to search for is
shown in Figure 2.9 and we would like to place a jump from the node Jump
to the node InLoop. However, in EIL (and IL) we do not have an instruction
corresponding to while; instead we have to identify a loop from the flow graph.
Figure 2.10 contains the logic program that performs this transformation.
The code has two parts: the first finds a suitable loop and the second builds the
jump.
Let us look at the conditions needed to find a loop. First we want to find a