Obfuscation from Low Noise Multilinear Maps

Multilinear maps enable homomorphic computation on encoded values and a public procedure to check if the computation on the encoded values results in a zero. Encodings in known candidate constructions of multilinear maps have a noise component, which is crucial for security. However, this noise grows (gets accumulated) with homomorphic computations and must remain below the maximal noise supported by the multilinear map for correctness. A smaller gap between the noise in the freshly generated encodings and the maximal noise supported is desirable. In this work, we put forward a new candidate construction of obfuscation based on GGH13 multilinear maps for which this gap is polynomial (in the security parameter). Our construction is obtained by tailoring GGH13 multilinear maps to a modification of the Lin’s [EUROCRYPT 2016] obfuscation construction. We prove the security of this variant of Lin’s construction in the hybrid graded encoding model that captures all known vulnerabilities of GGH13 maps and their conceivable extensions including the recent annihilation attacks of Miles, Sahai, and Zhandry [CRYPTO 2016].