Indistinguishability obfuscation, introduced by [Barak et. al. Crypto2001], 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 wellfounded assumptions. We prove: Informal Theorem: Let πβ (0,β), πΏβ (0,1), πβ (0,1) be arbitrary constants. Assume subexponential security of the following assumptions:  the Learning With Errors (LWE) assumption with subexponential modulustonoise ratio 2^{π^π} and noises of magnitude polynomial in π,where π is the dimension of the LWE secret,  the Learning Parity with Noise (LPN) assumption over general prime fields Zπ with polynomially many LPN samples and error rate 1/β^πΏ ,where β is the dimension of the LPN secret,  the existence of a Boolean PseudoRandom Generator (PRG) in NC0 with stretch π^{1+π}, where π is the length of the PRG seed,  the Decision Linear (DLIN) assumption on symmetric bilinear groups of prime order. Then, (subexponentially secure) indistinguishability obfuscation for all polynomialsize circuitsmore »
This content will become publicly available on April 26, 2023
Nonlinear Anti(ParityTime) Symmetric Dimer
In the present work we propose a nonlinear anti P T symmetric dimer, that at the linear level has been experimentally created in the realm of electric circuit resonators. We find four families of solutions, the socalled upper and lower branches, both in a symmetric and in an asymmetric (symmetrybroken) form. We unveil analytically and confirm numerically the critical thresholds for the existence of such branches and explore the bifurcations (such as saddlenode ones) that delimit their existence, as well as transcritical ones that lead to their potential exchange of stability. We find that out of the four relevant branches, only one, the upper symmetric branch, corresponds to a spectrally and dynamically robust solution. We subsequently leverage detailed direct numerical computations in order to explore the dynamics of the different states, corroborating our spectral analysis results.
 Award ID(s):
 2110030
 Publication Date:
 NSFPAR ID:
 10345508
 Journal Name:
 Frontiers in Physics
 Volume:
 10
 ISSN:
 2296424X
 Sponsoring Org:
 National Science Foundation
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