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An example: low outcome, or expectation in terms of game theory, can be the reason for a class of adversaries that are neither probabilistic quasi-polynomial nor PPT, and would only go after polynomial-logarithmic-time targets.


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I will answer this part specifically: Are there any practical differences between circuits and turing machines for cryptographic research (i.e. are there systems that are secure against PPT turing machines, but not polynomial-size circuits?) or does it exclusively come down to personal preference / convenience which one you use for your proofs? In ...


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Just looking for a Turing machine vs circuit is a bit misleading. The important distinction is uniform (complexity class BPP) vs non-uniform (complexity class P/poly) adversaries. You can characterize P/poly in terms of circuit families, but also in terms of Turing machines with arbitrary "advice strings." In fact, the latter is the more traditional ...



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