I would more willingly wager on the unbreakability of a Turing complete cryptosystem than one based on simple constructs from number theory.
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What if you encrypt encrypted data? One pass with AES256 and another with 3DES? The decryption effort would be exponential per layer.
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Exactly. Compose a bunch of standard and nonstandard crypto functions into an arbitrary program, so adversaries must crack the composition.
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And Turing complete systems can?
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Have you looked at any pqcrypto work? It relies on hardness assumptions based on hashing, etc, rather than factoring and discrete logs.
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Good intro by djb and Tanja Lange here:https://www.youtube.com/watch?v=-LlkJZJ5DMQ …
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