The coding theorems for the Shannon cipher system with a guessing wiretapper and correlated source outputs

The security level of the Shannon cipher system is traditionally measured by the equivocation 1/NH(Y|Z), where Y is a secret plaintext and Z is its cryptogram. But, Merhav and Arikan have considered another security criterion, which is measured by moments of the number of guesses needed for a wiretapper to uncover Y from Z. On the other hand, in the case of the traditional security criterion, Yamamoto has treated the coding problem with correlated source outputs X and Y such that only X is secret against wiretappers and only Y must be transmitted to a legitimate receiver. In this paper, we extend these two results and prove the coding theorems for the correlated source outputs in Merhav-Arikan's security criterion