On Obfuscating Set-Membership Predicate Functions

Obfuscation was first studied in computer programming field, which could be explained as a compiler that translates computer codes into an unintelligible form while preserving the original functionality. Since obfuscation for cryptographic purposes was raised out, several positive results have been presented in despite of the general impossibility. Secure obfuscation of point functions have been studied well and it was pointed out that secure composition of several point function obfuscation could realize the secure obfuscation of set-membership predicate function. However, secure composition of point function obfuscation was only proposed in one literature and the security was proved in Generic Group Model(GGM) under the definition of Virtual Grey Box-Obfuscation(VGB). In this paper we propose a new obfuscation construction of set-membership predicate functions under the standard definition of Virtual Black Box-Obfuscation(VBB). We utilize the vector space technique instead of obfuscation composition, and the security of obfuscation relies on an assumption which exists in standard model. Moreover, our obfuscation result of set-membership predicate functions can hide the real scale of the set and the obfuscation construction can be securely composed for different sets.