In this work, we introduce a new technique for taking a single-secret sharing scheme with a general access structure and transforming it into an individually secure multi-secret sharing scheme where every secret has the same general access structure. To increase the information rate, we consider Individual Security which guarantees zero mutual information with each secret individually, for any unauthorized subsets. Our approach involves identifying which shares of the single-secret sharing scheme can be replaced by linear combinations of messages. When $m-1$ shares are replaced, our scheme obtains an information rate of $m/|S|$, where $S$ is the set of shares. This provides an improvement over the information rate of $1/|S|$ in the original single-secret sharing scheme.

翻译：本文提出了一种新技术，可将具有一般访问结构的单秘密共享方案转化为个体安全的秘密共享方案，其中每个秘密均共享相同的访问结构。为提升信息率，我们采用个体安全概念，即对任意非授权子集，保证每个秘密的零互信息特性。该方法的核心在于识别单秘密共享方案中哪些份额可被消息的线性组合替代。当替换$m-1$个份额时，方案的信息率达到$m/|S|$（$S$为份额集合），相较于原始单秘密共享方案的$1/|S|$信息率实现了显著提升。