Information-Theoretically Secure Three-Party Computation with One   Corrupted Party
  The problem in which one of three pairwise interacting parties is required to securely compute a function of the inputs held by the other two, when one party may arbitrarily deviate from the computation protocol (active behavioral model), is studied. An information-theoretic characterization of unconditionally secure computation protocols under the active behavioral model is provided. A protocol for Hamming distance computation is provided and shown to be unconditionally secure under both active and passive behavioral models using the information-theoretic characterization. The difference between the notions of security under the active and passive behavioral models is illustrated through the BGW protocol for computing quadratic and Hamming distances; this protocol is secure under the passive model, but is shown to be not secure under the active model. 
Ye Wang, Prakash Ishwar, Shantanu Rane
cs.CR cs.IT math.IT