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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: Suppose there exists any set of constants\(\tau \in (0,\infty), \delta \in (0,1), \epsilon \in (0,1)\)such that the sub-exponential security of the following assumptions hold:—the Learning With Errors (\(\mathsf {LWE}\)) assumption with subexponential modulus-to-noise ratio\(2^{k^\epsilon }\)and noises of magnitude polynomial ink, wherekis the dimension of the\(\mathsf {LWE}\)secret,—the Learning Parity with Noise (\(\mathsf {LPN}\)) assumption over general prime fields\(\mathbb {Z}_p\)with polynomially many\(\mathsf {LPN}\)samples and error rate\(1/\ell ^\delta\), where\(\ell\)is the dimension of the\(\mathsf {LPN}\)secret,—the existence of a Boolean Pseudo-Random Generator (\(\mathsf {PRG}\)) in\(\mathsf {NC}^0\)with stretch\(n^{1+\tau }\), wherenis the length of the\(\mathsf {PRG}\)seed,—the Decision Linear (\(\mathsf {DLIN}\)) assumption on symmetric bilinear groups of prime order. Then, (subexponentially secure) indistinguishability obfuscation for all polynomial-size circuits exists. Furthermore, assuming only polynomial security of the aforementioned assumptions, there exists collusion resistant public-key functional encryption for all polynomial-size circuits.
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This content will become publicly available on August 31, 2026
Computing a Fixed Point of Contraction Maps in Polynomial Queries
We give an algorithm for finding an ε-fixed point of a contraction mapf: [0, 1]k\(\mapsto\)[0, 1]kunder the\(\ell _\infty\)-norm with query complexityO(klog (1/ε).
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- PAR ID:
- 10660612
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- Journal of the ACM
- Volume:
- 72
- Issue:
- 4
- ISSN:
- 0004-5411
- Page Range / eLocation ID:
- 1 to 20
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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