The emoji sequence is a hash of the secret key values generated as part of a modified/extended version of the Diffie-Hellman key exchange. The emoji sequence is generated and displayed independently on both devices before the final necessary key exchange message is transmitted over the wire, so a man-in-the-middle has no way of modifying messages in flight to ensure that both parties end up generating the same emoji sequence.

I'm not a cryptographer, but that's what I glean from their explanation: https://core.telegram.org/api/end-to-end/video-calls#key-ver...