Formal Verification of a Program Obfuscation Based on Mixed Boolean-Arithmetic Expressions


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.

Submitted Paper

This work has been submitted to CPP 2019.

Coq Development

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.

Installation Instructions


Browsable version of the Coq development

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".

Data structures, definitions and theorems used in many parts of the development

Compiler pass