0:00:00.000,0:00:02.000 The answer is the first one. 0:00:02.000,0:00:05.000 Bob should compute yA to the xB power modulo q. 0:00:05.000,0:00:07.000 The second one would compute the same thing. 0:00:07.000,0:00:09.000 This is in fact exactly what Alice computed, 0:00:09.000,0:00:12.000 but Bob can't do this because he doesn't know xA. 0:00:12.000,0:00:14.000 The third one wouldn't compute the same key, 0:00:14.000,0:00:19.000 so the correctness property is that Alice and Bob obtain the same key, 0:00:19.000,0:00:21.000 and we can show this by just plugging in the values. 0:00:21.000,0:00:25.000 The key Alice computed was yB to the xA. 0:00:25.000,0:00:28.000 The value of yB is g to the xB, so that's equivalent 0:00:28.000,0:00:31.000 to g to the xB xA mod q. 0:00:31.000,0:00:34.000 The key that Bob would compute--and we'll write that as key BA 0:00:34.000,0:00:38.000 since we haven't yet shown that they're equivalent using this equation. 0:00:38.000,0:00:44.000 Well, yA is g to the xA, so this is g to the xA xB mod q. 0:00:44.000,0:00:47.000 And we already showed that powers of powers are commutative, 0:00:47.000,9:59:59.000 so these two are equivalent.