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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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2 Answers 2


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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I suggest you read Post Quantum Cryptography

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Hi, James, and welcome to Crypto Stack Exchange. Please note that we would generally prefer good answers here to consist of more than just a link. If you've read the book, perhaps you could summarize the relevant aspects of it (like, say, which ciphers it describes, and what their major advantages and drawbacks are)? Also, instead of linking to a Google Books result, perhaps a link to, say, the publisher's official page -- and/or to pqcrypto.org -- might be better? –  Ilmari Karonen 8 hours ago

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