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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 (growing) noise component, which is crucial for security. For example, noise in GGH13 multilinear maps grows with the number of levels that need to be supported and must remain below the maximal noise supported by the multilinear map for correctness. A smaller maximal noise, which must be supported, is desirable both for reasons of security and efficiency.

In this work, we put forward new candidate constructions of obfuscation for which the maximal supported noise is polynomial (in the security parameter). Our constructions are obtained by instantiating a modification of Lin’s obfuscation construction (EUROCRYPT 2016) with composite order variants of the …