Non-cryptographic hashing using carry-less multiplication and associated methods, software, and apparatus. Under one aspect, the disclosed hash solution expands on CRC technology that updates a polynomial expansion and final reduction, to use initialization (init), update and finalize stages with extended seed values. The hash solutions operate on input data partitioned into multiple blocks comprising sequences of byte data, such as ASCII characters. During multiple rounds of an update stage, operations are performed on sub-blocks of a given block in parallel including carry-less multiplication and shuffle operations. During a finalize stage, multiple SHA or carry-less multiplication operations are performed on data output following a final round of the update stage.