A Provable Scheme for Homomorphic Obfuscations in Software Security

and C. Thomborson (New Zealand)


software obfuscation, residue number coding, homomor phic obfuscation.


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, cryptosys tems, etc. Software obfuscation is one of these measures. It protects software from unauthorized modification by mak ing software more obscure so that it is hard for the poten tial attacker to understand the obfuscated software. In soft ware 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 origi nal program to hide the true meaning of these variables [2]. There is some discussion about the divisionof residue num bers in [2], but the technique proposed there is incorrect. In this paper, we establish a provable residue number encod ing for software obfuscation, especially a provable algo rithm for division by several constants in residue numbers.

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