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 P. 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.
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