Statistical security conditions for two-party secure function evaluation

To simplify proofs in information-theoretic security, the standard security definition of two-party secure function evaluation based on the real/ideal model paradigm is often replaced by an information-theoretic security definition. At EUROCRYPT 2006, we showed that most of these definitions had some weaknesses, and presented new information-theoretic conditions that were equivalent to a simulation-based definition in the real/ideal model. However, there we only considered the perfect case, where the protocol is not allowed to make any error, which has only limited applications. We generalize these results to the statistical case, where the protocol is allowed to make errors with a small probability. Our results are based on a new measure of information that we call the statistical information, which may be of independent interest.