Secure Multi-Party Computation from Strongly Uniform Key Agreement.

We construct Indistinguishability Obfuscation ((mathsf {iO})) and Functional Encryption ((mathsf {FE})) schemes in the Turing machine model from the minimal assumption of compact (mathsf {FE}) for circuits ((mathsf {CktFE})). Our constructions overcome the barrier of sub-exponential loss incurred by all prior work. Our contributions are:1.We construct (mathsf {iO}) in the Turing machine model from the same assumptions as required in the circuit model, namely, sub-exponentially secure (mathsf {FE}) for circuits. The previous best constructions [6, 41] require sub-exponentially secure (mathsf {iO}) for circuits, which in turn requires sub-exponentially secure (mathsf {FE}) for circuits [5, 15].2.We provide a new construction of single input (mathsf {FE}) for Turing machines with unbounded length inputs and optimal parameters from polynomially secure, compact (mathsf {FE}) for circuits. The previously best known construction by Ananth and Sahai [7] relies on (mathsf {iO}) for circuits, or equivalently, sub-exponentially secure (mathsf {FE}) for circuits.3.We provide a new construction of multi-input (mathsf {FE}) for Turing machines. Our construction supports a fixed number of encryptors (say k), who may each encrypt a string (mathbf {x}_i) of unbounded length. We rely on sub-exponentially secure (mathsf {FE}) for circuits, while the only previous construction [10] relies on a strong knowledge type assumption, namely, public coin differing inputs obfuscation.