A data generation apparatus includes a processor that executes a process including obtaining target data sequentially from time-series data, the target data including n (n being an integer greater than or equal to 2) data items in a predetermined section of the time-series data, calculating parameter information satisfying a (k−1) order polynomial based on the target data, the (k−1) order polynomial including k random values, k being an integer greater than or equal to 1 and less than n, associating the target data to the parameter information, outputting the target data and the parameter information associated to the target data, attaching a signature to secret information based on a secret distributed protocol. The secret information is calculable by using k pairs of data including the target data and the parameter information associated to the target data, and outputting the secret information attached with the signature.