Probabilistic Certification of Divide & Conquer Algorithms

In [6], a new approach for certifying the correctness of program executions in hostile environments has been proposed. The authors presented probabilistic certification by massive attack detection through two algorithmsMCT and EMCT . The execution to certify is represented by a macro-dataflow graph which is used to randomly extract some tasks to be re-executed on safe resources in order to determine whether the execution is correct or faulty. Bounds associated with certification have been provided for general graphs and for tasks with out-tree dependencies. In this paper, we extend those results with a cost analysis of parallel certification based on on-line scheduling by work-stealing. In particular, we focus on Divide & Conquer algorithms that are commonly used in symbolic computations and demonstrate the efficiency of EMCT for the certification of the resulting Fork-Join graph. Finally, we show how to combine EMCT with BCH codes to make a matrixvector product both tolerant to falsifications and massive attacks.