Zero-error information and applications in cryptography

In analogy to the zero-error variant of the channel capacity, the zero-error information between two random variables is defined. We show that our definition is natural in the sense that the representation of the channel capacity with respect to mutual information carries over to the zero-error variants of the quantities. It is shown that the new notion, together with two operators introduced in the same context, namely the common random variable of two random variables and the dependent part of a random variable with respect to another, is useful for giving characterizations of the possibility of realizing cryptographic tasks - such as bit commitment, coin tossing, or oblivious transfer - from correlated pieces of information.