Tampering of a database can be detected through the use of cryptographically-strong hash functions. Subsequently-applied forensic analysis algorithms can help determine when, what, and perhaps ultimately who and why. This paper presents a novel forensic analysis algorithm, the Tiled Bitmap Algorithm, which is more efficient than prior forensic analysis algorithms. It introduces the notion of a candidate set (all possible locations of detected tampering(s)) and provides a complete characterization of the candidate set and its cardinality. An optimal algorithm for computing the candidate set is also presented. Finally, the implementation of the Tiled Bitmap Algorithm is discussed, along with a comparison to other forensic algorithms in terms of space/time complexity and cost. An example of candidate set generation and proofs of the theorems and lemmata and of algorithm correctness can be found in the appendix.