Obfuscating straight line arithmetic programs

Program Obfuscation that renders any given program essentially equivalent to a black box, while desirable, is impossible [4] in the general polynomial time adversary models. It is natural to search for positive results under restricted programs (e.g., point functions [20, 2] POBDDs [10], cryptographic primitives [17, 12, 13]. Here we study straight line arithmetic programs. Our model of obfuscation requires an attacker to produce the entire code only by looking at the obfuscated program. We show that obfuscation is possible, assuming factoring is hard and we have access to a tamper-resistant hardware (or secure token). We also assume that the programs can be sampled from some distribution. Our results are based on extending a result due to Shamir \cite{Sha93} on generation of hard to factor polynomials to straight line programs.