Hash-based asymmetrical encryption (not digital signature) schemes? In the Wikipedia article or another article about post-quantum crypto there's a plenty of information about hash-based signatures. But where are hash-based ecryption with pubkey?


  But, over the long-term, it's generally confidentiality (i.e. encryption) that you need to maintain and I haven't talked about post-quantum encryption at all in this post. (Maybe in the future.)


Why articles about hash-based asymmetric encryption are more hard to come by?

Possible reasons:


It is impossible and the proof is basic enough that it not deserves an article (or a question here)
It is even more impractical than hash-based signatures
It is secret and classified
It is somehow not interesting and nobody cared to research it
It is called by some other term, using which articles get found easily.
Linked articles actually do speak about them, but I don't read attentively and missed it.
It's impossible to construct a strong asymmetric encryption algorithm that relies only on the security of a hash function:


  We prove that every key exchange protocol in the random oracle model in which the honest users make at most n queries to the oracle can be broken by an adversary making O(n^2) queries to the oracle.


Boaz Barak, Mohammad Mahmoody-Ghidary - Merkle Puzzles are Optimal

(The proof assumes the attacker is only limited by the number of hash computations and has unlimited computational power otherwise)

The quadratic advantage of Merkle Puzzles is not sufficient to achieve the security and performance levels expected of modern cryptography. For example at a security level of 80 bits (Breaking it is equivalent to about one day of bitcoin mining), the defenders would need to exchange terabytes of information and need an hour or so of computation.

And against quantum computers you don't even get that quadratic advantage.