Paper 2015/693

Foundations of Reactive Garbling Schemes

Jesper Buus Nielsen and Samuel Ranellucci

Abstract

Garbled circuits is a cryptographic technique, which has been used among other things for the construction of two and three-party secure computation, private function evaluation and secure outsourcing. Garbling schemes is a primitive which formalizes the syntax and security properties of garbled circuits. We define a generalization of garbling schemes called \emph{reactive garbling schemes}. We consider functions and garbled functions taking multiple inputs and giving multiple outputs. Two garbled functions can be linked together: an encoded output of one garbled function can be transformed into an encoded input of the other garbled function without communication between the parties. Reactive garbling schemes also allow partial evaluation of garbled functions even when only some of the encoded inputs are provided. It is possible to further evaluate the linked garbled functions when more garbled inputs become available. It is also possible to later garble more functions and link them to the ongoing garbled evaluation. We provide rigorous definitions for reactive garbling schemes. We define a new notion of security for reactive garbling schemes called confidentiality. We provide both simulation based and indistinguishability based notions of security. We also show that the simulation based notion of security implies the indistinguishability based notion of security. We present an instantiation of reactive garbling schemes. We present an application of reactive garbling schemes to reactive two-party computation secure against a malicious adversary. We demonstrate how garbling schemes can be used to give abstract black-box descriptions and proof of several advanced applications of garbled circuits in the literature, including Minilego and Lindell's forge-and-loose technique.