Neither! The statement he is 'awfully sure of' is a probalistic conclusion he has derived from experimental evidence via Bayesian reasoning on the world's first programmable computer. Specifically, that statement is this:

"The Nipponese cryptosystem that we call Azure is the same thing as the German system that we call Pufferfish," he announces. "Both of them are also related somehow to another, newer cryptosystem I have dubbed Arethusa. All of these have something to do with gold. Probably gold mining operations of some sort. In the Philippines."

Part of the argument used to convince Comstock:

"But those places send out thousands of messages a day," Comstock protests. "What makes you think that you can pick out the messages that are a consequence of the Azure orders?"

"It's just a brute force statistics problem," Waterhouse says. "Suppose that Tokyo sent the Azure message to Rabaul on October 15th, 1943. Now, suppose I take all of the messages that were sent out from Rabaul on October 14th and I index them in various ways: what destinations they were transmitted to, how long they were, and, if we were able to decrypt them, what their subject matter was. Were they orders for troop movements? Supply shipments? Changes in tactics or procedures? Then, I take all of the messages that were sent out from Rabaul on October 16th--the day after the Azure message came in from Tokyo--and I run exactly the same statistical analysis on them."

Waterhouse steps back from the chalkboard and turns into a blinding fusillade of strobe lights. "You see, it is all about information flow. Information flows from Tokyo to Rabaul. We don't know what the information was. But it will, in some way, influence what Rabaul does afterwards. Rabaul is changed, irrevocably, by the arrival of that information, and by comparing Rabaul's observed behavior before and after that change, we can make inferences."