Title: Annihilation Attacks for Multilinear Maps: Cryptanalysis of Indistinguishability Obfuscation over GGH13

Friday, April 1, 2016 - 10:30am to 12:00pm
MIT, Hewlett G882, 32 Vassar St, Gates Tower
Mark Zhandry
Abstract: In this work, we put forward a new class of polynomial-time attacks on the original multilinear maps of Garg, Gentry, and Halevi (2013). Previous polynomial-time attacks on GGH13 generally required the availability of low-level encodings of zero. Most significantly, such attacks were not applicable to candidate indistinguishability obfuscation (iO) schemes. 

We introduce annihilation attacks, which attack multilinear maps using non-linear polynomials. Annihilation attacks can work in situations where there are no low-level encodings of zero. Using annihilation attacks, we give the first polynomial-time cryptanalysis of candidate iO schemes over GGH13. More specifically, we exhibit two simple programs that are functionally equivalent, and show how to efficiently distinguish between the obfuscations of these two programs.  We also show that annihilation attacks are applicable to candidate Order Revealing Encryption schemes built over GGH13.

* Joint work with Eric Miles and Amit Sahai