Optimally Indifferentiable Double-Block-Length Hashing Without Post-processing and with Support for Longer Key Than Single Block

摘要

Existing double-block-length (DBL) hash functions, in order to achieve optimal indifferentiable security (security up to O(2~n) query complexity), require a block cipher with n-bit blocks and k-bit keys such that 2n ≤ k, and a post-processing function with two block cipher calls. In this paper, we consider the indifferentiability of MDPH, a combination of the MDP domain extender and Hirose's compression function. MDPH does not require the post-processing function (thus has better efficiency), and supports block ciphers with n < k. We show that MDPH achieves (nearly) optimal indifferentiable security. To the best of our knowledge, this is the first result for DBL hashing with optimal indifferentiable security, with support for block ciphers with n < k, and without the post-processing function.