基于良好假设的不可否认性混淆
Indistinguishability Obfuscation from Well-Founded Assumptions
摘要：
在这项工作中，我们将展示如何构建不可混淆性混淆从次指数硬度的四个有根据的假设。证明了：设$τ\in (0,\infty), δ\in (0,1), ε\in (0,1)$为任意常数.假设以下假设的次指数安全性，其中$λ$是安全参数，并且以下参数$\ell,k,n$是$λ$中足够大的多项式：- 对具有次指数模噪声比$2^{k^ε}$的$\mathbb{Z}_{p}$的LWE假设，其中$k$是LWE秘密的维数，- 在具有多项式多个LPN样本和错误率$1/\ell^δ$的$\mathbb{Z}_p$上的LPN假设，其中$\ell$是LPN秘密的维度，-在具有拉伸$n^{1+τ}$的$\mathsf{NC}^0$中存在布尔PRG，然后，存在针对所有多项式大小电路的（亚指数安全的）不可混淆性混淆。
英文摘要：
In this work, we show how to construct indistinguishability obfuscation from subexponential hardness of four well-founded assumptions. We prove: Let $τ\in (0,\infty), δ\in (0,1), ε\in (0,1)$ be arbitrary constants. Assume sub-exponential security of the following assumptions, where $λ$ is a security parameter, and the parameters $\ell,k,n$ below are large enough polynomials in $λ$: - The SXDH assumption on asymmetric bilinear groups of a prime order $p = O(2^λ)$, - The LWE assumption over $\mathbb{Z}_{p}$ with subexponential modulus-to-noise ratio $2^{k^ε}$, where $k$ is the dimension of the LWE secret, - The LPN assumption over $\mathbb{Z}_p$ with polynomially many LPN samples and error rate $1/\ell^δ$, where $\ell$ is the dimension of the LPN secret, - The existence of a Boolean PRG in $\mathsf{NC}^0$ with stretch $n^{1+τ}$, Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exists.
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