ECCC-Report TR20-126https://eccc.weizmann.ac.il/report/2020/126Comments and Revisions published for TR20-126en-usWed, 19 Aug 2020 14:37:19 +0300
Paper TR20-126
| Indistinguishability Obfuscation from Well-Founded Assumptions |
Aayush Jain,
Huijia Lin,
Amit Sahai
https://eccc.weizmann.ac.il/report/2020/126In this work, we show how to construct indistinguishability obfuscation from subexponential hardness of four well-founded assumptions. We prove:
Let $\tau \in (0,\infty), \delta \in (0,1), \epsilon \in (0,1)$ be arbitrary constants. Assume sub-exponential security of the following assumptions, where $\lambda$ is a security parameter, and the parameters $\ell,k,n$ below are large enough polynomials in $\lambda$:
- The SXDH assumption on asymmetric bilinear groups of a prime order $p = O(2^\lambda)$,
- The LWE assumption over $\mathbb{Z}_{p}$ with subexponential modulus-to-noise ratio $2^{k^\epsilon}$, where $k$ is the dimension of the LWE secret,
- The LPN assumption over $\mathbb{Z}_p$ with polynomially many LPN samples and error rate $1/\ell^\delta$, where $\ell$ is the dimension of the LPN secret,
- The existence of a Boolean PRG in $\mathsf{NC}^0$ with stretch $n^{1+\tau}$,
Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exists.Wed, 19 Aug 2020 14:37:19 +0300https://eccc.weizmann.ac.il/report/2020/126