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Kindly comments on I played as AI in AI Box, and it was generally frustrating all around. - Less Wrong Discussion
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It's worth noting that for the most part, we don't. Aside from highly limited techniques such as one-time pads, we merely have cryptographic tools for demanding information from adversaries with bounded computational power in ways that simply cannot be cheated as long as we assume one of several hardness conjectures.
"with bounded computational power" - if that limited computational power means that even if every atom in the known Universe was a computer, it would still take more than the age of the Universe to brute-force it... then it is safe to assume that even the most superintelligent AI couldn't break it.
I think we're saying the same thing? With the added correct clarification "as long as we assume one of several hardness conjectures."
I work in cryptography, I'm aware of its limitations. But this application is within the scope of things that are currently being worked on...