In this work, we present a modification of a well-established measure of dependence appropriate for the analysis of stopping times for adversarial processes on cryptographic primitives. We apply this measure to construct generic criteria for the ideal behavior of fixed functions in both the random oracle and ideal permutation setting. More significantly, we provide a nontrivial extension of the notion of hash function indifferentiability, transporting the theory from the status of providing security arguments for protocols utilizing ideal primitives into the more realistic setting of protocol assurance with fixed functions. The methodology this measure introduces to indifferentiability analysis connects the security of a hash function with an indifferentiable mode to the security of the underlying compression function in a quantitative way; thus, we prove that dependence results on cryptographic primitives provide a direct means of determining the practical resistance or vulnerability of protocols employing such primitives.
"A measure of dependence for cryptographic primitives relative to ideal functions." Rocky Mountain J. Math. 45 (4) 1283 - 1309, 2015. https://doi.org/10.1216/RMJ-2015-45-4-1283