I would more willingly wager on the unbreakability of a Turing complete cryptosystem than one based on simple constructs from number theory.
Exactly. Compose a bunch of standard and nonstandard crypto functions into an arbitrary program, so adversaries must crack the composition.
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Radios in the US Military use synchronized frequency hopping. I wonder if its feasible for crypto to use synchronized algorithm hopping?
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Without the key (like a random seed value), you wouldn't know the hop period or the selected algorithm.
End of conversation
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