Indistinguishability Obfuscation Without Multilinear Maps: New Paradigms via Low Degree Weak Pseudorandomness and Security Amplification

Abstract

The existence of secure indistinguishability obfuscators (Formula Presented) has far-reaching implications, significantly expanding the scope of problems amenable to cryptographic study. All known approaches to constructing (Formula Presented) rely on d-linear maps. While secure bilinear maps are well established in cryptographic literature, the security of candidates for (Formula Presented) is poorly understood. We propose a new approach to constructing (Formula Presented) for general circuits. Unlike all previously known realizations of (Formula Presented), we avoid the use of d-linear maps of degree (Formula Presented). At the heart of our approach is the assumption that a new weak pseudorandom object exists. We consider two related variants of these objects, which we call perturbation resilient generator ((Formula Presented) RG) and pseudo flawed-smudging generator ((Formula Presented)), respectively. At a high level, both objects are polynomially expanding functions whose outputs partially hide (or smudge) small noise vectors when added to them. We further require that they are computable by a family of degree-3 polynomials over (Formula Presented). We show how they can be used to construct functional encryption schemes with weak security guarantees. Finally, we use novel amplification techniques to obtain full security. As a result, we obtain (Formula Presented) for general circuits assuming: Subexponentially secure LWEBilinear Maps(Formula Presented) -secure 3-block-local PRGs(Formula Presented) RGs or (Formula Presented) s