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Large-scale sensor-based decision support systems are being widely deployed. Assessing the trustworthiness of sensor data and the owners of this data is critical for quality assurance of decision making in these systems. Trust evaluation frameworks use data provenance along with the sensed data values to compute the trustworthiness of each data item. However, in a sizeable multi-hop sensor network, provenance information requires a large and variable number of bits in each packet, which, in turn, results in high energy dissipation with extended period of radio communication, making trust systems unusable. We propose an energy-efficient provenance transmission and construction scheme, which we refer to as Probabilistic Provenance Flow (PPF). To the best of our knowledge, ours is the first approach to make the Probabilistic Packet Marking (PPM) approach of IP traceback feasible for sensor networks. We propose two bit-efficient complementary provenance encoding and construction methods, and combine them to handle topological changes in the network. Our TOSSIM simulations demonstrate that PPF requires at least 33% fewer packets and consumes 30% less energy than PPM-based approaches to construct provenance, yet still provides high accuracy in trust score calculation.