The complexity of human computation via a concrete model with an application to passwords

What can humans compute in their heads? We are thinking of a variety of cryptographic protocols, games like sudoku, crossword puzzles, speed chess, and so on. For example, can a person compute a function in his or her head so that an eavesdropper with a powerful computer-who sees the responses to random inputs-still cannot infer responses to new inputs? To address such questions, we propose a rigorous model of human computation and associated measures of complexity. We apply the model and measures first and foremost to the problem of 1) humanly computable password generation and then, consider related problems of 2) humanly computable "one-way functions" and 3) humanly computable "pseudorandom generators." The theory of human computability developed here plays by different rules than standard computability; the polynomial vs. exponential time divide of modern computability theory is irrelevant to human computation. In human computability, the step counts for both humans and computers must be more concrete. As an application and running example, password generation schemas are humanly computable algorithms based on private keys. Humanly computable and/or humanly usable mean, roughly speaking, that any human needing-and capable of using-passwords can if sufficiently motivated generate and memorize a secret key in less than 1 h (including all rehearsals) and can subsequently use schema plus key to transform website names (challenges) into passwords (responses) in less than 1 min. Moreover, the schemas have precisely defined measures of security against all adversaries, human and/or machine.

人类可以在脑海中计算什么？我们正在考虑各种加密协议，例如Sudoku，填字游戏，Speed Chess等。例如，一个人可以计算自己的头部功能，以便具有强大计算机的窃听器 - 看到对随机输入的响应无法推断出对新输入的响应吗？为了解决此类问题，我们提出了一种严格的人类计算模型和相关的复杂度量。我们首先将模型和衡量标准应用于1）可计算的密码生成的问题，然后考虑2）可计算的“单向功能”和3）可计算的“伪和生成器”。在这里开发的人类计算性理论与标准可计算性不同。现代计算理论的多项式与指数时间差与人类计算无关。在人类的可计算性中，人类和计算机的步骤计数必须更具体。作为一个应用程序和运行的示例，密码生成模式是基于私钥的可计算算法。大致说，人类可以计算和/或人类可用的意思是，如果有足够的动机产生并记住秘密钥匙在不到1小时（包括所有彩排），则可以使用passwords的任何人（包括所有彩排），并且可以随后使用schema Plus Plus Key在不到1分钟的时间内将网站名称（挑战）转换为密码（响应）。此外，模式具有针对所有对手，人类和/或机器的确切定义的安全措施。