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.
Silaghi, M.C. (2004). Improving arithmetic circuits for solving constraint satisfaction and optimization problems (CS-2004-14). Melbourne, FL. Florida Institute of Technology.