A Provable Scheme for Homomorphic Obfuscations in Software Security

Computer and communication industries develop so rapidly that the demand for software becomes larger and larger and the demand for software protections, such as copyright and anti-tampering defense, are more and more important to software users and developers. There are some technical measures for software protections, such as hardware-based protections, network filters, cryptosystems, etc. Software obfuscation is one of these measures. It protects software from unauthorized modification by making software more obscure so that it is hard for the potential attacker to understand the obfuscated software. In software obfuscation, we can obfuscate the control flow and the data flow of the software. In this paper, we explore an obfuscation based on residue number coding, which is a method widely used in hardware design, high precision integer arithmetic, and cryptography [1]. Recently, it has used as an obfuscation that encoded variables in the original program to hide the true meaning of these variables [2]. There is some discussion about the division of residue numbers in [2], but the technique proposed there is incorrect. In this paper, we establish a provable residue number encoding for software obfuscation, especially a provable algorithm for division by several constants in residue numbers.