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What can humans compute in their heads? We are thinking of a variety ofCrypto Protocols, games like Sudoku, Crossword Puzzles, Speed Chess, and so on.The intent of this paper is to apply the ideas and methods of theoreticalcomputer science to better understand what humans can compute in their heads.For example, can a person compute a function in their head so that aneavesdropper with a powerful computer --- who sees the responses to randominput --- still cannot infer responses to new inputs? To address suchquestions, we propose a rigorous model of human computation and associatedmeasures of complexity. We apply the model and measures first and foremost tothe problem of (1) humanly computable password generation, and then considerrelated problems of (2) humanly computable "one-way functions" and (3) humanlycomputable "pseudorandom generators".  The theory of Human Computability developed here plays by different rulesthan standard computability, and this takes some getting used to. For reasonsto be made clear, the polynomial versus exponential time divide of moderncomputability theory is irrelevant to human computation. In humancomputability, the step-counts for both humans and computers must be moreconcrete. Specifically, we restrict the adversary to at most 10^24 (Avogadronumber of) steps. An alternate view of this work is that it deals with theanalysis of algorithms and counting steps for the case that inputs are small asopposed to the usual case of inputs large-in-the-limit.

The Complexity of Human Computation: A Concrete Model with an Application to Passwords