At current date the problem of how to build distributed and replicated Software Transactional Memory (STM) to enhance both dependability and performance is still largely unexplored. This paper fills this gap by presenting D2STM, a replicated STM whose consistency is ensured in a transparent manner, even in the presence of failures. Strong consistency is enforced at transaction commit time by a non-blocking distributed certification scheme, which we name BFC (Bloom Filter Certification). BFC exploits a novel Bloom Filter-based encoding mechanism that permits to significantly reduce the overheads of replica coordination at the cost of a user tunable increase in the probability of transaction abort. Through an extensive experimental study based on standard STM benchmarks we show that the BFC scheme permits to achieve remarkable performance gains even for negligible (e.g. 1%) increases of the transaction abort rate.