Diffie-Hellman Key Exchange

1 - Diffie-Hellman on prime field

Alice	Bob
Public share
$F_{p}, p =$	$g =$
Secret
Secret $a =$	Secret $b =$

$x = g^{a} \mod p =$	$y = g^{b} m o d p =$
Shared secret
$k = g^{a b} \mod p =$

2 - Diffie-Hellman on elliptic curve

Alice	Bob
Public share
Elliptic curve $y^{2} = x^{3} + x + 7$ and $F_{p}, p = 83$	Generator $G (0, 16)$
Secret
Secret $a =$	Secret $b =$

$A = a G =$	$B = b G =$
Shared secret
$K = a b G =$