Indistinguishability Obfuscation from Well-Founded Assumptions

Indistinguishability obfuscation, introduced by [Barak et. al. Crypto’2001], aims to compile programs into unintelligible ones while preserving functionality. It is a fascinating and powerful object that has been shown to enable a host of new cryptographic goals and beyond. However, constructions of indistinguishability obfuscation have remained elusive, with all other proposals relying on heuristics or newly conjectured hardness assumptions. In this work, we show how to construct indistinguishability obfuscation from subexponential hardness of four well-founded assumptions. We prove: Theorem: Let τ∈(0,∞),δ∈(0,1),ϵ∈(0,1) be arbitrary constants. Assume sub-exponential security of the following assumptions, where λ is a security parameter, p is a λ -bit prime, and the parameters ℓ,k,n are large enough polynomials in λ : - the Learning With Errors ( LWE ) assumption over Zp with subexponential modulus-to-noise ratio 2kϵ , where k is the dimension of the LWE secret, -

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• Darya Kaviani