The insertion of expressions mixing arithmetic operators and bitwise boolean operators is a widespread protection of sensitive data in source programs. This recent advanced obfuscation technique is one of the less studied among program obfuscations even if it is commonly found in binary code. In this paper, we formally verify in Coq this data obfuscation. It operates over a generic notion of mixed boolean-arithmetic expressions and on properties of bitwise operators operating over machine integers. Our obfuscation performs two kinds of program transformations: rewriting of expressions and insertion of modular inverses. To facilitate its proof of correctness, we define boolean semantic tables, a data structure inspired from truth tables.
Our obfuscation is integrated into the CompCert formally verified compiler where it operates over Clight programs. The automatic extraction of our program obfuscator into OCaml yields a program with competitive results.
This work has been submitted to CPP 2019.
The development has been made with Coq 8.8.2 and OCaml 4.06.1. The sources are available here.
Note: the sources contain a modified version of CompCert 3.4. CompCert also requires the Menhir parser generator. Refer to the CompCert manual for detailed information.
tar -xvf CompCert-3.4-obf.tar.xz.
./configurewith appropriate options (refer to the manual) then
make installto install the
ccomp file.c -o file -mbaobf cfg.mbawill compile an obfuscated version of
file.cto using the obfuscation intructions in the file
-dclightwill output an obfuscated C version of
cfg.mba. You can run
ccomp test.c -o test -mbaobf cfg.mba -dclightat the root of the folder, and observe the obfuscation in the file
cfg.mba), each line corresponds to an obfuscation pass, and contains 4 integers :
"a;b;c;d". This intruction will obfuscate the
ath expression (Breadth-first search of the AST of the program) using the
bth rewrite rule, then introduce the affine function
(2*c+1)x + dand its inverse around the freshly obfuscated expression.
The documentation gives a commented listing of the Coq specifications and proofs for the main development files. Proof scripts are folded by default, but can be viewed by clicking on "Proof".