In response to the issues of low security and reliability associated with video steganography, a video steganography algorithm is proposed based on a pseudo-random number generator (PRNG). The PRNG is utilized for selecting video frames, thereby enhancing the randomness and unpredictability of the steganographic process. The sequence generated by the PRNG, unlike traditional fixed-pattern frame selection, is difficult to predict, making it challenging for attackers to infer the embedding strategy from external features, thereby reducing the likelihood of detection by statistical analysis tools and machine learning models. Additionally, check digit lattice coding is employed to encode secret data into redundant information, enhancing the integrity of the secret data and improving its resistance to interference in complex communication environments. Experimental results demonstrate that this algorithm significantly enhances the security and concealment of video steganography, and effectively resists statistical analysis attacks. Moreover, while maintaining a high data embedding rate, it ensures a low error rate and high image quality.