Herein, we propose generating CAPTCHAs through random field simulation and give a novel, effective and efficient algorithm to do so. Indeed, we demonstrate that sufficient information about word tests for easy human recognition is contained in the site marginal probabilities and the site-to-nearby-site covariances and that these quantities can be embedded directly into certain conditional probabilities, designed for effective simulation. The CAPTCHAs are then partial random realizations of the random CAPTCHA word. We start with an initial random field (e.g., randomly scattered letter pieces) and use Gibbs resampling to re-simulate portions of the field repeatedly using these conditional probabilities until the word becomes human-readable. The residual randomness from the initial random field together with the random implementation of the CAPTCHA word provide significant resistance to attack. This results in a CAPTCHA, which is unrecognizable to modern optical character recognition but is recognized about 95% of the time in a human readability study.

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Contemporary real-time problems like CAPTCHA generation and optical character recognition can be solved effectively using correlated random fields. These random fields should be produced on a graph in order that problems of any dimension and shape can be handled. However, traditional solutions are often too slow, inaccurate or both. Herein, the Quick Simulation Random Field algorithm to produce correlated random fields on general undirected graphs is introduced. It differs from prior algorithms by completing the graph and setting the unspecified covariances to zero, which facilitates analytic study. The Quick Simulation Random Field graph distribution is derived within and the following questions are studied: (1) For which marginal pmfs and covariances will this algorithm work? (2) When does the marginal property hold, where the sub-graph distribution of an algorithm-simulated field matches the distribution of the algorithm-simulated field on the subgraph? (3) When does the permutation property hold, where the vertex simulation order does not affect the joint distribution?

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