Abstract
In a (<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>)-threshold secret image sharing (SIS) scheme, a secret image is encoded into <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> shadow images and distributed to the corresponding participants, enabling lossless reconstruction with any <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> correct shadow images. This inherent fault tolerance allows up to <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>β<inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> shadow images to be lost or corrupted. However, in real-world scenarios, all shadow images are susceptible to malicious tampering, cropping, or noise during transmission and storage, making it difficult to guarantee the availability of <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> intact shadows. Robust secret image sharing (RSIS) schemes have been proposed to address this issue, yet existing methods often suffer significant degradation in reconstruction quality as the attack strength increases, revealing limitations in their robustness. To address these issues, we propose an RSIS scheme against malicious shadow images by Reusing Polynomial Coefficients with hash function (RSIS-RPC), which provides both malicious shadow detection and error correction capabilities. The correction capability improves with the degree of coefficient reuse, where greater reuse provides stronger resilience to pixel corruption. However, as more coefficients are reused, the size of the generated shadow images increases correspondingly, resulting in higher storage requirements. This trade-off between robustness and efficiency makes the proposed scheme adaptable to diverse application scenarios requiring secure and resilient image sharing. Experimental results and analyses demonstrate that the proposed scheme achieves superior robustness compared to existing schemes.