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This paper studies trust mining in the framework of keyed MapReduce and trust computing in the context of the Bayesian inferences and makes the following two-fold contributions: In the first fold, a general method for trust mining is introduced and formalized in the context of keyed MapReduce functions. A keyed MapReduce function is a classic MapReduce function associated with a common reference keyword set so that a document is projected on the specified common reference set rather the whole dictionary as that defined in the classic MapReduce function. As a result, keyed MapReduce functions allow one to define flexible trust mining procedures: a look-up table which records the comments of neighbors can be constructed from the inverted index of the keyed MapReduce function; In the second fold, a new method for trust computing is introduced and formalized in the context of maximum likelihood distribution. A look-up table generated in the trust mining stage is now viewed as the current state of the target server and then the maximum likelihood distribution over the look-up table is deduced. We show that the proposed trust computing mechanism is optimal (an upper bound of trust values).