Adaptive Succinct Garbled RAM or: How to Delegate Your Database.

We show how to garble a large persistent database and then garble, one by one, a sequence of adaptively and adversarially chosen RAM programs that query and modify the database in arbitrary ways. The garbled database and programs reveal only the outputs of the programs when run in sequence on the database. Still, the runtime, space requirements and description size of the garbled programs are proportional only to those of the plaintext programs and the security parameter. We assume indistinguishability obfuscation for circuits and somewhat-regular collision-resistant hash functions. In contrast, all previous garbling schemes with persistent data were shown secure only in the static setting where all the programs are known in advance. As an immediate application, we give the first scheme for efficiently outsourcing a large database and computations on the database to an untrusted server, then delegating computations on this database, where these computations may update the database. Our scheme extends the non-adaptive RAM garbling scheme of Canetti and Holmgren [ITCS 2016]. We also define and use a new primitive of independent interest, called adaptive accumulators. The primitive extends the positional accumulators of Koppula et al. [STOC 2015] and somewhere statistical binding hashing of Hubáă﾿ek and Wichs [ITCS 2015] to an adaptive setting.