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In the recent years we have proposed a set of secure multiparty computations for solving distributed constraint satisfaction and optimization problems, with applications to areas like distributed scheduling, configurations, team-making, and auctions. Some of the newest versions were based on an arithmetic circuit for selecting a random element out of the elements with a given value in a (secret) array. Here we show how to improve that arithmetic circuit by a factor of at least 4. The improvement is based on an optimization of the functions and on the usage of CSP solvers to exploit public constraints.

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