Lower Bounds on Assumptions Behind Indistinguishability Obfuscation

Since the seminal work of Garg et al. (FOCS’13) in which they proposed the first candidate construction for indistinguishability obfuscation (iO for short), iO has become a central cryptographic primitive with numerous applications. The security of the proposed construction of Garg et al. and its variants are proved based on multi-linear maps (Garg et al. Eurocrypt’13) and their idealized model called the graded encoding model (Brakerski and Rothblum TCC’14 and Barak et al. Eurocrypt’14). Whether or not iO could be based on standard and well-studied hardness assumptions has remain an elusive open question. In this work we prove lower bounds on the assumptions that imply iO in a black-box way, based on computational assumptions. Note that any lower bound for iO needs to somehow rely on computational assumptions, because if P = NP then statistically secure iO does exist. Our results are twofold:

• Type: Journal
• Year: 2016
• Where: TCC
• Authors: Mohammad Mahmoody, Ameer Mohammed, Soheil Nematihaji, Rafael Pass, Abhi Shelat
• Keywords: Cryptology, TCC 2016