Keyless Signature Infrastructures as a secure Post-Quantum Scheme I came across a company that relies on hashing, similar to block chain technology.  They explicitly stated in their white paper that hash based cryptographic schemes are inherently post-quantum schemes.

Counter to this, is an article co-authored by Schneier (linked in blog post) that lends support to the idea of Grover's algorithm enabling cryptanalysis of "Keyless Signature Infrastructure" (KSI).  Is the position that KSI is inherently a PQC scheme tenable simply because no conventional device is known to have broken it?

It seems like this argument is sleight of hand, given it does not rely on a security reduction of an NP-Hard problem which as I understand is essential to any PQC scheme.  Is their use of a modified blockchain method actually post-quantum secure?
I would just like to know on what basis they can say it is PQC without any NP problem reduction.


I believe that the point you're making is assuming that a Quantum Computer could solve any problem in NP that's not actually NP-complete quickly (or, at least, in polynomial time).  That's not known to be true; Quantum Computers would be able to solve some problems (such as factorization) in polynomial time, if $P \ne NP$, there's a whole range of problems in NP that's neither P nor NP-complete.