BLE - Numeric comparison

[Roei]

Hi,

How does numeric comparison works? Shouldn't both devices share parameters in order to display the same number? How can we be protected from MITM?

Thanks!

[Dmitry]

Hi,

function g2 includes both public keys. In case of MITM attack, one side will have PK(Alice)+PK(Eve), other side - PK(Eve)+PK(Bob), numbers will never match.

[Roei]

Ok,

So the random number is generated from diffie-hellman key?

[Dmitry]

g2 uses both public keys and exchanged random numbers, not an ECDH secret:

[Roei]

Thanks!

One more question - I assume the basic diffie-hellman (modulu functions) and elliptic curve diffie hellman work differently, but the idea of using public and private key and generating shared secret it the same, right?

[Dmitry]

Exactly.