NUSS:Non-Interactive Updatable of Secret Sharing Schemes Using Homomorphic Encryption

Secret sharing schemes (SSS) are essential for distributed cryptography due to their role in safeguarding sensitive data. They face significant challenges in maintaining longterm security, especially in dynamic environments that require frequent updates to shares, such as in cloud storage systems where data is continually modified and accessed by multiple parties. While proactive secret sharing (PSS) addresses this issue through periodic share renewal, current methods necessitate extensive inter-party communication, resulting in high bandwidth usage and increased vulnerability to synchronization attacks. Moreover, these interactive update processes risk leaking sensitive information, including threshold structures. Motivated by these challenges, we propose NUSS (Non-Interactive Updatable Secret Sharing), a novel approach leveraging homomorphic encryption for non-interactive updates of secret shares. Our method encrypts shared arrays homomorphically, enabling share updates within the encrypted domain without requiring share regeneration and redistribution. Specifically, the update process is conducted via homomorphic computation, which works directly on the ciphertext. This approach ensures data security and minimizes communication complexity, allowing each party to complete the update process independently using encrypted share arrays. Experimental evaluation confirms that NUSS effectively mitigates the risk of information leakage compared to traditional proactive secret sharing. Additionally, our proposal requires only n secure channels, significantly reducing communication costs by lowering the number of secure channels required from O(n<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>) in traditional PSS to O(n).