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Is SRP-6a post-quantum secure? If it is not post-quantum secure, do any post-quantum secure alternatives similar to SRP-6a exist?

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No, since finding $a$ allows offline checking of passwords. $\:$ No, although I can't back this part up.

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  • $\begingroup$ Thanks for this! I assume the second "no" refers to post-quantum secure "SRP-6a-like" alternatives, right? Does S/KEY or a similar alternative based on Lamport's scheme provide such a security? $\endgroup$ – mpr Aug 2 '14 at 14:53
  • $\begingroup$ That is what it refers to. $\:$ For S/KEY, I think a commitment scheme that is one-to-one non-malleable, extractable, and equivocable would suffice, although the only candidates for that which I can think of use at least multi-string setup. $\:$ What is "a similar alternative based on Lamport's scheme"? $\;\;\;\;$ $\endgroup$ – user991 Aug 3 '14 at 5:25
  • $\begingroup$ Thanks for the paper! I'll be sure to read it :) Regarding "a similar alternative based on Lamport's scheme", what I meant was using the one-way property of cryptographic hashes based on a common secret. Would you mind extending your comment on the S/KEY alternatives into an answer? Thank you very much for your time! $\endgroup$ – mpr Aug 5 '14 at 13:02
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The problem arises from the fact that the security of the SRP protocol heavily relies on the hardness of the discrete logarithm problem. And as was shown by Shor the discrete logarithm problem can be broken by quantum computers in the near future.

Post-Quantum Secure Remote Password Protocol from RLWE Problem describes one possible solution using a RLWE-based SRP protocol (RLWE-SRP) which inherits the advantages from SRP and the elegant design from an RLWE key exchange. Additionally the reference implementation of the protocol is said to be significantly faster than the original SRP for a 112-bits of security.

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  • $\begingroup$ Link-only answers are generally discouraged. Could you maybe summarize the content of the linked paper? $\endgroup$ – Maeher Mar 5 at 9:11

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