In that case we are perfectly fine. We can distribute symmetric keys in a different way. Just run a hash 10,000,000 times and your public key will be the last result, while the private key will be the first input. Only you can reconstruct the other layers going backwards, as you “peel the onion” and you can use those numbers any way you want. My favorite application is to generate random numbers among untrusting participants by everyone revealing the next number and then using functions of that as seeds to an RNG. It can be used for tons of byzantine fault tolerant applications.

The only problem is that it seems to also have forward secrecy built in because once you’ve revealed the next onion layer, anyone could have constructed the transcript up to that point. So you can only be sure that the author signed something if you are sure they didn’t reveal the next private key to anyone else (to verify it).

This doesn't work for encryption, though. You'd need a cryptosystem where it's possible to encrypt a message with H(x) such that it can only (efficiently) be decrypted given x, for a hash function H. To the best of my knowledge, no such hash function is known.

It’s an open question whether hash functions can be used for encryption using XOR:

https://crypto.stackexchange.com/questions/35809/whats-wrong...

Here is a basic explanation:

https://cryptography.fandom.com/wiki/Snuffle

Note however that you would need a nonce / salt transmitted with each message because otherwise decrypting messages encrypted with the same key would just be as easy as XORing them!

Snuffle is symmetric key encryption, and yes, it's a well-known construction. However, you previously suggested that an asymmetric encryption scheme (with public and private keys) could be constructed using a hash.

oh, right. It’s only good for signing and random number generation, not encryption.

Still that’s plenty useful! It can be used for blockchains and crypto currency.