A method of an aspect includes receiving an instruction indicating a first source having at least one set of four state matrix data elements, which represent a complete set of four inputs to a G function of a cryptographic hashing algorithm. The algorithm uses a sixteen data element state matrix, and alternates between updating data elements in columns and diagonals. The instruction also indicates a second source having data elements that represent message and constant data. In response to the instruction, a result is stored in a destination indicated by the instruction. The result includes updated state matrix data elements including at least one set of four updated state matrix data elements. Each of the four updated state matrix data elements represents a corresponding one of the four state matrix data elements of the first source, which has been updated by the G function.