Systems, methods, and apparatuses relating to performing hashing operations on packed data elements are described. In one embodiment, a processor includes a decode circuit to decode a single instruction into a decoded single instruction, the single instruction including at least one first field that identifies eight 32-bit state elements A, B, C, D, E, F, G, and H for a round according to a SM3 hashing standard and at least one second field that identifies an input message; and an execution circuit to execute the decoded single instruction to: rotate state element C left by 9 bits to form a rotated state element C, rotate state element D left by 9 bits to form a rotated state element D, rotate state element G left by 19 bits to form a rotated state element G, rotate state element H left by 19 bits to form a rotated state element H, perform two rounds according to the SM3 hashing standard on the input message and state element A, state element B, rotated state element C, rotated state element D, state element E, state element F, rotated state element G, and rotated state element H to generate an updated state element A, an updated state element B, an updated state element E, and an updated state element F, and store the updated state element A, the updated state element B, the updated state element E, and the updated state element F into a location specified by the single instruction.