The quantum key distribution (QKD) network with Vernam’s one-time pad encryption and secret sharing are powerful security tools to realize an information theoretically secure (ITS) distributed storage system. In the work of Fujiwara et al., a single-password-authenticated secret sharing (SPSS) scheme based on the QKD network and Shamirs secret sharing was experimentally demonstrated; it confirmed ITS data transmission, storage, authentication, and integrity. To achieve data integrity, an ITS message authentication code (MAC) tag is employed, and a data owner of the secret sharing performs both the MAC tag generation and verification. However, for a scenario in which the data owner and end users are different entities, the above approach may not work, since the data owner can cheat the end users. In this article, we resolve this problem by proposing an ITS integrity protection scheme employing a third-party verification with time-stamp. The ITS integrity protection is realized by two steps: integrity check by the data owner at data reconstruction and data integrity certification by the data owner, the end user, and the third-party verifier using a MAC based on universal2 hash function and random number provided from the QKD network. In addition to introducing the third-party verifier, we institute “a trusted calculator,” which computes shares of the data and MAC tags and sends MAC tags to the third-party verifier. The random number used in calculation is stored in the trusted calculator. We implement this scheme on the SPSS system installed in the Tokyo QKD Network.