# MPC on boolean circuits

I am reading about Yao's and GMW protocols and was wondering if there is any perfectly secure MPC protocol in the semi-honest setting, where the underlying circuit is a Boolean circuit (eg. n=3 and t=1)?

You can easily embed a Boolean circuit into the field $$GF[2^k]$$ for any $$k$$. Once you have done this embedding, you can then run any perfectly secure protocol. However, note that perfect security requires $$t and so a minimum of 4 parties (with 1 corruption). For $$n=3$$ and $$t=1$$, it is possible to get statistical security.

Note that for the specific case of $$n=3$$ and $$t=1$$ you can also use a dedicated for Boolean circuits. For semi-honest adversaries, one example is High-Throughput Semi-Honest Secure Three-Party Computation with an Honest Majority.