We show that it is possible to upgrade an obfuscator for a weak complexity class
into an obfuscator for arbitrary polynomial size circuits, assuming that the class
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
implies the existence of general-purpose obfuscators for
. 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
. Our reduction works with respect to virtual black-box obfuscators and relativizes to ideal models..