Techniques are provided for generating a hash value for searching for substrings in a data stream without reading more than one element (e.g. one byte) at a time. According to one technique, a before a next element is added to an old hash value, the old hash value is circularly shifted one or more bits. The first original element is shifted a number of bits and XOR'ed against the old hash value. The next element is added to the old hash value. In one embodiment, an entry value is retrieved for each element from an index table and the XOR and shift operations are performed on the entry values. According to another technique, each Linear Feedback Shift Register (LFSR) of a plurality of LFSRs read in one element at a time beginning at different offsets. Each LFSR uses the same state machine. The result of reading a number of elements into an LFSR is used as the hash value.