International Association
for Cryptologic Research

We show that it is possible to upgrade an obfuscator for a weak complexity class $\\weak$ into an obfuscator for arbitrary polynomial size circuits, assuming that the class $\\weak$ can compute pseudorandom functions. Specifically, under standard intractability assumptions (e.g., hardness of factoring, Decisional Diffie--Hellman, or Learning with Errors), the existence of obfuscators for $\\NC^1$ or even $\\TC^0$ implies the existence of general-purpose obfuscators for $\\classP$. Previously, such a bootstrapping procedure was known to exist under the assumption that there exists a fully-homomorphic encryption whose decryption algorithm can be computed in $\\weak$. Our reduction works with respect to virtual black-box obfuscators and relativizes to ideal models.