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My question is a follow-up to a recent question regarding quantum-secure time-lock puzzles (TLPs). TLPs can be built (in principle) from indistinguishability obfuscation (iO) [BGJ+,BGL+] as noted in this thread. As a corollary, quantum-secure iO would lead to quantum-secure TLPs (provided that there are inherently-sequential languages in the quantum world, which seems plausible).

So it boils down to whether any of the candidate constructions of iO are quantum-secure. It seems that some of the candidates are broken given a quantum computer [PM]. The question is whether any remaining candidate construction of iO is believed/conjectured to be quantum-secure?

[BGJ+]: Bitansky et al., Time-Lock Puzzles from Randomized Encodings, ITCS'16

[BGL+]: Bitansky et al., Succinct Randomized Encodings and their Applications, STOC'15

[PM]: Pellet-Mary, Quantum Attacks against Indistinguishablility Obfuscators Proved Secure in the Weak Multilinear Map Model, Crypto'18

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Turns out that this was an open question. Brakerski et al. [BDGM] posted a paper today on the ePrint claiming the first (provable) post-quantum construction of iO. Their underlying security assumption is the "circular security" of an encryption scheme based on LWE.

[BDGM], Brakerski, Döttling, Garg and Malavolta, Factoring and Pairings are not Necessary for iO: Circular-Secure LWE Suffices, ePrint Archive

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