Mixed Boolean-Arithmetic (MBA) Obfuscation Using Permutation Polynomials on Modular Lipschitz Integers

Mixed Boolean-Arithmetic (MBA) Obfuscation Using Permutation Polynomials on Modular Lipschitz Integers

연구 분야: Analysis

학회: 2024 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE)

In 2007 Zhou et al. introduced a powerful software obfuscation technique using Mixed Boolean-Arithmetic (MBA) expressions and a special family of permutation polynomials on the modular integer ring {{\mathbb{Z}}_{{2^n}}} (integers modulo 2n or unsigned integers of n-bit width). Since then MBA-based software obfuscation has attracted considerable interest in industry and the scientific research community. In this paper, we introduce new families of permutation polynomials by extending Zhou’s techniques to the non-commutative ring of modular Lipschitz integers {{\mathbb{L}}_{{2^n}}}. Permutation polynomials on the non-commutative ring {{\mathbb{L}}_{{2^n}}} can be interpreted as invertible multivariate transformations on the modular integer ring {{\mathbb{Z}}_{{2^n}}} and therefore the newly introduced permutation polynomials of this paper greatly expand the variety of invertible polynomial transformations on {{\mathbb{Z}}_{{2^n}}} that can be used for MBA-based software obfuscation and potentially other applications such as whitebox cryptography.