Can't be done for public key encryption, but it is a beautiful thing for public key digital signatures (seals). https://sphincs.cr.yp.to/
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P.S. BLAKE2 is a good secure hash function.
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There is work on hash-based signatures (with benefits of being post-quantum) see eg https://huelsing.wordpress.com/hash-based-signature-schemes/literature/ …
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Merkle trees are a simple PK *signature* scheme (with some practical issues.)
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You're missing a few ingredients there I think. Usually you need a trapdoor function too.
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I don't think secure hashes have the properties that make a problem suitable for pub key crypto.
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I am a crypto-amateur, but AFAIK secure hashes can typically be exchanged for others within a PKC, so you cannot infer much from it.
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I tried solving int factorization a while ago. I'd guess it's possible to generate one-way functions, but I was satisfied enough for now.
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