Obfuscation of Abstract Data-Types - Rowan

CHAPTER 2. OBFUSCATIONS FOR INTERMEDIATE LANGUAGE 35
replace var (OldVar,
NewVar,
replace vertex(OldVert,NewVert) : nil
) :−
exists ({ }∗ ;
{ ′ set(OldVar,OldVal)}
) (entry,OldVert),
listof (OldEdge,source(OldVert,OldEdge),OldEdges),
@vlabel(OldVert,instr label(Labels, )),
assign fn(OldVal,NewVal),
build assign(Labels,NewVar,NewVal,OldEdges,NewVert).
build assign(Labs,L,R,Edges,Vert) :−
@new vertex(instr label(Labs,exp(expr type(assign(L,R),
int(true,b32)))),
Edges,Vert).
Figure 2.6: Predicates for replacing assignments
Finding a suitable array
We need to find a vertex InitVert which has an array initialisation of the form:
OldArray := newarr(Type)[Size]
where OldArray is a local variable of array type.
For this transformation to be applicable, we ensure that every path through
our method goes through InitVert and that the array is always used with its
index (except at the initialisation) — so for example, we cannot pass the whole
array to another method. We can write this safety condition as follows:
safe to transform(InitVert,OldArray) :−
all ({ }∗ ;
{ ′ isnode(InitVert) } ;
{ not( ′ unindexed(OldArray)) }∗
) (entry,exit).
The predicate unindexed(OldArray,E) holds if OldArray is used without an
index at the node pointed to by edge E. We define unindexed by pattern
matching to EIL expressions. So, for example:
unindexed(A,A).
unindexed(exp(E),A) :− unindexed(E,A).
unindexed(expr type(E,T),A) :− unindexed(E,A).
unindexed(arrayindex(L,R),A) :− not(L = A), unindexed(L,A).
unindexed(arrayindex(L,R),A) :− unindexed(R,A).
After a suitable array has been found we need to create initialisations for
our two new arrays with the correct sizes.