Result by Amos Beimel, Ariel Gabizon, Yuval Ishai, Eyal Kushilevitz, Sigurd Meldgaard, Anat Paskin-Cherniavsky
The authors consider the case of non-interactive secure computation. This basically means we view the protocol as consisting of n-1 parties sending a single message to a referee party, which then output the result of the computation. The authors consider results for semi-honest adversaries in the information theoretical setting and achieve unconditional results for the best possible robustness we could hope for, for some type of functions. However, because of the non-interactivity their results should extend easily to the malicious case (using unconditionally secure one-time MACs). In particular the functions they achieve unconditional results for are multiplication of group elements and functions polynomial in the size of the input domain. For symmetric functions they achieve the same results, but with less strict robustness. The authors also prove negative results when using private simultaneous messages protocols and garbling schemes. The authors also considers relations of NIMPC and obfuscation along with multi input functional encryption. The presentation includes many of these results along with constructive proofs and are a bit to cumbersome to go through in this blog, so I will recommend having a look at the paper for details.