An operation apparatus includes a message expansion unit, a state data initiation unit, a state data generation unit, and a chain variable update unit. The message expansion unit generates a plurality of expanded messages using a message. The state data initiation unit generates the initial value of state data using chain variable data. The state data generation unit generates the final value of the state data by iterating a combination function and a step function using the state data and the plurality of expanded messages. The chain variable update unit updates the chain variable data using the state data of the final value.