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Privacy requirements can be modeled within the distributed constraint satisfaction framework, where the constraints are secrets of the participants. In [20] we introduced a first technique allowing agents to solve distributed constraint problems (DisCSPs), without revealing anything and without trusting each other or some server. The first technique we propose now, MPC-DisCSP2, is a dm times improvement for m variables of domain size d. A second technique we propose, MPC-DisCSP3, has a similar complexity as MPD-DisCSP2, a little slower in the worst case, but guarantees that the returned solutions are picked according to a uniform distribution over the total set of solutions. A third technique, MPC-DisCSP0, is based solely on secure arithmetic circuit evaluation and the distribution for picking its solutions can be manipulated in a more flexible way. Nevertheless this last technique has a O(d **m factorial times d **m) complexity. All techniques of [20] can be extended to solve optimization for distributed weighted CSPs.

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