Paper 2019/1025 Original: eprint.iacr.org/2019/1025 ↗

On Perfect Correctness without Derandomization

Abstract

We give a method to transform any indistinguishability obfuscator that suffers from correctness errors into an indistinguishability obfuscator that is $\textit{perfectly}$ correct, assuming hardness of Learning With Errors (LWE). The transformation requires sub-exponential hardness of the obfuscator and of LWE. Our technique also applies to eliminating correctness errors in general-purpose functional encryption schemes, but here it is sufficient to rely on the polynomial hardness of the given scheme and of LWE. Both of our results can be based $\textit{generically}$ on any perfectly correct, single-key, succinct functional encryption scheme (that is, a scheme supporting Boolean circuits where encryption time is a fixed polynomial in the security parameter and the message size), in place of LWE. Previously, Bitansky and Vaikuntanathan (EUROCRYPT ’17) showed how to achieve the same task using a derandomization-type assumption (concretely, the existence of a function with deterministic time complexity $2^{O(n)}$ and non-deterministic circuit complexity $2^{\Omega(n)}$) which is non-game-based and non-falsifiable.