The navigation signal authentication schemes protect GNSS services from spoofing attacks by attaching unforgeable information to signals. In this study, Randomly Flipped Chip based Signal Power Authentication (RFC‐SPA), is proposed to jointly authenticate the navigation message and spreading code of GNSS civilian signals. Designed to support two modes of authentication (fast channel and slow channel), the proposed scheme employs a fixed amount of flipped chips, which are randomly distributed in some areas of the spreading code to form a relative fluctuation in the correlation result of the signal. The fast channel is a spreading code authentication (SCA) of these flipped chips, which is the same as the Chimera. In the slow channel, since the correlation results between the local periodical spreading code and the signal in areas with flipped chips will be smaller than those results in areas without flipped chips, receivers in the tracking correlation can extract this fluctuation. Since the fluctuation modulates a digital signature, receivers can verify the authenticity of both the navigation message and spreading code through the authentication of this digital signature. Compared with mainstream schemes, RFC‐SPA requires no extra tracking channel and has no impact on the navigation message. Besides, the proposed scheme maintains a similar robustness and security performance while significantly reducing the storage requirement compared with SCA. The scheme is demonstrated in a proposed implementation for Beidou B1C civilian signal, and the performance metrics are analysed. In the proposed implementation, the detection possibility is higher than 99.7% at 35dBHz of C/N0, and only 33.6% of the storage is required compared with the suggested configuration of the Chimera scheme for the GPS L1C civilian signal.