Khan reads fast, and they gave him access to the ship's library computers while he was in sickbay. Given his nature, it's likely that in addition to reading about the state of the Federation's science and technology, Khan also reviewed political and military history for the period he was sleeping.
I don't know if it's ever stated, but it's possible that when they dumped Khan and his followers on Ceti Alpha 3 (or 4 or 5 or whatever it was), they gave them some sort of library computer and he might've found the information in there.
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