Optimization of Tree Modes for Parallel Hash Functions : A case study

International audienceThis paper focuses on parallel hash functions based on tree modes of operation for a compression function. We discuss the various forms of optimality that can be obtained when designing such parallel hash functions. The first result is a scheme which optimizes the tree topology in order to decrease at best the running time. Then, without affecting the optimal running time we show that we can slightly change the corresponding tree topology so as to decrease at best the number of required processors as well. Consequently, the resulting scheme optimizes in the first place the running time and in the second place the number of required processors. The present work is of independent interest if we consider the problem of parallelizing the evaluation of an expression where the operator used is neither associative nor commutative