Secure function evaluation for Boolean formulae
For log-depth circuits, it is possible to use an information-theoretic version of Yao's garbled circuits. Note that in a garbled gate, each key is used to encrypt twice. Thus, if the keys on the input wires are double the length of the keys on the output wires, then one-time pad encryption can be used and the result is information theoretically secure. 

See the paper Gate Evaluation Secret Sharing and Secure One-Round Two-Party Computation by Vlad Kolesnikov, and references within.