One of the basic tasks in bioinformatics is localizing a short subsequence (S), read while sequencing, in a long reference sequence (R), like the human geneome. A natural rapid approach would be finding a hash value for (S) and compare it with a prepared database of hash values for each of length (|S|) subsequences of (R). The problem with such approach is that it would only spot a perfect match, while in reality there are lots of small changes: substitutions, deletions and insertions. This issue could be repaired if having a hash function designed to tolerate some small distortion accordingly to an alignment metric (like Needleman-Wunch): designed to make that two similar sequences should most likely give the same hash value. This paper discusses construction of Distortion-Resistant Hashing (DRH) to generate such fingerprints for rapid search of similar subsequences. The proposed approach is based on the rate distortion theory: in a nearly uniform subset of length (|S|) sequences, the hash value represents the closest sequence to (S). This gives some control of the distance of collisions: sequences having the same hash value.