While provably secure steganography provides strong concealment by ensuring stego carriers are indistinguishable from natural samples, such systems remain vulnerable to real-world edit errors (e.g., insertions, deletions, substitutions) because their decoding depends on perfect synchronization and lacks error-correcting capability. To bridge this gap, we propose Alkaid, a provably secure steganographic scheme resilient to edit errors via distance-constrained encoding. The key innovation integrates the minimum distance decoding principle directly into the encoding process by enforcing a strict lower bound on the edit distance between codewords of different messages. Specifically, if two candidate codewords violate this bound, they are merged to represent the same message, thereby guaranteeing reliable recovery. While maintaining provable security, we theoretically prove that Alkaid offers deterministic robustness against bounded errors. To implement this scheme efficiently, we adopt block-wise and batch processing. Extensive experiments demonstrate that Alkaid achieves decoding success rates of 99\% to 100\% across diverse error channels, delivers a payload of 0.2 bits per token for high embedding capacity, and maintains an encoding speed of 6.72 bits per second, significantly surpassing state-of-the-art (SOTA) methods in robustness, capacity, and efficiency.

翻译：尽管可证明安全隐写术通过确保隐写载体与自然样本不可区分来提供强隐蔽性，但此类系统在实际编辑错误（例如插入、删除、替换）面前仍然脆弱，因为其解码过程依赖于完美同步且缺乏纠错能力。为弥补这一差距，我们提出了Alkaid，一种通过距离约束编码实现对编辑错误鲁棒的可证明安全隐写方案。其核心创新在于通过强制不同消息码字之间的编辑距离具有严格下界，将最小距离解码原理直接集成到编码过程中。具体而言，若两个候选码字违反此界限，则将其合并以表示同一消息，从而保证可靠恢复。在保持可证明安全性的同时，我们从理论上证明了Alkaid对有限错误具有确定性鲁棒性。为实现该方案的高效运行，我们采用了分块与批处理技术。大量实验表明，Alkaid在多种错误信道下实现了99%至100%的解码成功率，以每词元0.2比特的负载提供高嵌入容量，并保持6.72比特/秒的编码速度，在鲁棒性、容量和效率方面显著超越了现有最优方法。