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

The existence of secure indistinguishability obfuscators (iO) has far-reaching implications, significantly expanding the scope of problems amenable to cryptographic study. All known approaches to constructing iO rely on d-linear maps. While secure bilinear maps are well established in cryptographic literature, the security of candidates for d > 2 is poorly understood. We propose a new approach to constructing iO for general circuits. Unlike all previously known realizations of iO, we avoid the use of d-linear maps of degree d >= 3. 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 (Delta RG) and pseudo flawed-smudging generator (PFG), 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 Z. 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 iO for general circuits assuming: - Subexponentially secure LWE - Bilinear Maps - poly(lambda)-secure 3-block-local PRGs - Delta RGs or PFGs