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Web-based computing (WBC) is a modality of collaborative computing wherein "volunteers" register at a Web site, receiving one (usually compute-intensive) task to compute at each visit and returning the results from that task at the subsequent visit. The security of a WBC project is enhanced if the owner of the Web site can easily keep track of which "volunteer" computed which tasks, thereby endowing the project with accountability. We develop a framework for constructing computationally lightweight schemes for endowing WBC projects with accountability. The framework is built around the notion of a directly computed task allocation function (TAF) that reserves a dedicated subset of the Web site's tasks for each "volunteer." We show how TAFs simplify the data structures needed to link "volunteers" with their tasks, even when "volunteers" are allowed to join and leave the WBC project dynamically. We then design a methodology for constructing easily computed TAFs that enhance the efficiency of the accountability scheme.