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It's well-known that Shor's algorithm can solve integer factorization, discrete logarithm and discrete log over elliptic curves in cubic time. This implies that cryptosystems like RSA, ElGamal, and Elliptic Curve Diffie-Hellman (ECDH) are vulnerable to quantum computers.

Are there any existing public-key cryptosystem that are NOT known to have a polynomial-time quantum attack?

This question was inspired by this blog post.

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I suggest you read Post Quantum Cryptography –  James Junghanns 2 days ago

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If you mean "syntactically public key" instead of "implies the existence of secure key agreement",
then there is also hash-based signatures.

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