In 1992, Frankel and Desmedt introduced a technique that enables one to reduce the secret space of an ideal homomorphic secret sharing scheme (IHSSS) into any of its characteristic subgroups. In this paper, we propose a similar technique to reduce the secret space of IHSSSs called the quotient technique. By using the quotient technique, we show that it is possible to yield an ideal linear scheme from an IHSSS for the same access structure, providing an alternative proof of a recent result by Jafari and Khazaei. Moreover, we introduce the concept of decomposition of secret sharing schemes. We give a decomposition for IHSSSs, and as an application, we present a necessary and sufficient condition for an IHSSS to be mixed-linear. Continuing this line of research, we explore the decomposability of some other scheme classes.

1992 年，Frankel 和 Desmedt 引入了一种技术，可以将理想同态秘密共享方案 (IHSSS) 的秘密空间减少到其任何特征子群中。在本文中，我们提出了一种类似的技术来减少 IHSSS 的秘密空间，称为商技术。通过使用商技术，我们表明可以从 IHSSS 为相同的访问结构产生理想的线性方案，为 Jafari 和 Khazaei 的最近结果提供替代证明。此外，我们引入了秘密共享方案分解的概念。我们给出了 IHSSS 的分解，并且作为一个应用，我们给出了 IHSSS 是混合线性的充分必要条件。继续这条研究路线，我们探索了一些其他方案类的可分解性。