Cryptography Stack Exchange is a question and answer site for software developers, mathematicians and others interested in cryptography. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|improve this question
I suggest you read Post Quantum Cryptography – James Junghanns May 23 '15 at 9:45


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

share|improve this answer

Since the time you asked your question some new algorithms have shown great promise. The first set of algorithms are based on the Learning with Errors Problem in over polynomial rings. See

There is also an elliptic curve scheme based around supersingular elliptic curve isogenies. There's a Wikipedia article on that.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.