New Negative Results on Differing-Inputs Obfuscation

We provide the following negative results for differing-inputs obfuscation (diO): (1) If subexponentially secure one-way functions exist then sub-exponentially secure diO for TMs does not exist (2) If in addition sub-exponentially secure iO exists then polynomially secure diO for TMs does not exist. 1 Department of Computer Science & Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA. Email: [email protected]. URL: https://cseweb.ucsd.edu/~mihir/. Supported in part by NSF grants CNS-1526801 and CNS-1228890, ERC Project ERCC FP7/615074 and a gift from Microsoft. 2 Department of Computer Science & Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA. Email: [email protected]. URL: https://cseweb.ucsd.edu/~istepano/. Supported in part by NSF grants CNS-1526801 and CNS-1228890, ERC Project ERCC FP7/615074 and a gift from Microsoft. 3 Department of Computer Science, University of Texas at Austin, 2317 Speedway, Austin, Texas 78712, USA. Email: [email protected]. URL: https://www.cs.utexas.edu/~bwaters/. Supported in part by NSF grants CNS-1228599 and CNS-1414082, DARPA SafeWare, a Google Faculty Research award, the Alfred P. Sloan Fellowship, a Microsoft Faculty Fellowship and a Packard Foundation Fellowship.