Can two parties agree on a secret while everyone listens? Some parts of Ethereum depend on that stronger kind of assumption. Others, like ordinary account signatures, don't.
The idea: A plain one-way function lets you lock something that only you can open later, but not something a stranger can lock for you, or a secret two strangers can agree on in public. For that the problem needs extra structure: a hidden shortcut (a trapdoor, as in RSA), or a way for two secrets to combine (as in Diffie-Hellman). The second needs less: Diffie-Hellman gives encryption without any trapdoor. Impagliazzo and Rudich showed that no straightforward ("black-box") construction gets this from a one-way function alone, which is why it's a separate, stronger bet.
Why it matters: Shows which pieces of Ethereum would survive if public-key encryption turned out to be impossible.
On the map: needs more than one-way functions (Cryptomania). If impossible, every KE-tagged assumption falls: P2P handshakes, BLS consensus, KZG blobs, BN254 SNARKs. ECDSA accounts (ECDLP only), hashes and STARKs survive
The assumption that two parties can agree on a secret over a public channel, or encrypt to a public key. It needs more than one-way functions[1, 2].
On this map, the assumptions tagged KE each give key exchange on their own: curve Diffie-Hellman (used in peer-to-peer handshakes), co-CDH and q-SDH on BLS12-381 (BLS signatures, KZG), and the q-type assumptions on BN254 (SNARK verifiers). If public-key encryption were impossible, all of those would fall.
What would survive: ECDSA accounts, which rest on discrete log alone, plus every hash-based component: Merkle-Patricia tries, SSZ, STARKs and all the hash-based post-quantum plans.
If any of these breaks, this breaks too.
If this breaks, these break with it.