you don't have to fake the voice, just mitm and record cleartext

But they have to fake the voice, if I call the other person and say "my emoji sequence is this, this and that" for the other person to verify and vice-versa.

Person A calls you. I intercept the call, so person A is calling me, and then I call you (spoofing so I look like Person A). When you pick up, I pick up, then I transmit what you're saying to Person A (and vice versa).

How do you know I'm intercepting the transmission? Does the emoji sequence verify the call, perhaps?

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...

The emoji sequence represents the secret key exchange between you and the other party. If you intercept the call, you are making one key exchange with person A, and another key exchange with person B. Due to the mathematics involved, there is no way for you to force both key exchanges to yield the same result.

For a "standard" DH key exchange it would be possible to brute force the emoji sequence to be the same (since it's too short to be resistant to brute forcing), but the protocol that Telegram uses specifically defends against that by having both sides commit to their share of the key ahead of time, so they cannot try different numbers.

https://core.telegram.org/api/end-to-end/video-calls#key-ver...

So person A and person B are going to see different emojis no matter what you do. To fake a phone verification while performing a main-in-the-middle attack you'd also have to fake their voices to each other. That's hard.

Both connections would show different emojis on both sides then. So you would need to somehow deep fake the voice of the one telling their emojis to the other one.

If i'm talking to a person I know in person, I'd recognise their voice.