Indistinguishability Obfuscation from DDH-Like Assumptions on Constant-Degree Graded Encodings

Huijia Lin, Vinod Vaikuntanathan
2016 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)  
All constructions of general purpose indistinguishability obfuscation (IO) rely on either meta-assumptions that encapsulate an exponential family of assumptions (e.g., Pass, Seth and Telang, CRYPTO 2014 and Lin, EUROCRYPT 2016), or polynomial families of assumptions on graded encoding schemes with a high polynomial degree/multilinearity (e.g., Gentry, Lewko, Sahai and Waters, FOCS 2014). We present a new construction of IO, with a security reduction based on two assumptions: (a) a DDH-like
more » ... ption -called the joint-SXDH assumption -on constant degree graded encodings, and (b) the existence of polynomial-stretch pseudorandom generators (PRG) in NC 0 . Our assumption on graded encodings is simple, has constant size, and does not require handling composite-order rings. This narrows the gap between the mathematical objects that exist (bilinear maps, from elliptic curve groups) and ones that suffice to construct general purpose indistinguishability obfuscation.
doi:10.1109/focs.2016.11 dblp:conf/focs/LinV16 fatcat:4ht5vc7b55ehphb2vrc24xkneq