A secret sharing scheme is a cryptographic technique to protect a secret from loss and leakage by dividing it into shares. A ramp secret sharing scheme can improve efficiency in terms of the information ratio by allowing partial information about the secret which is composed of several sub-secrets to leak out. The notion of strong security has been introduced to control the amount of information on every subset of the sub-secrets that unauthorized sets can obtain. However, there have been proposed few methods to construct strongly secure schemes for general access structures. Furthermore, all existing methods need strong assumptions, which lead to a loss of efficiency and a limitation of access structures. In this paper, we show that any ramp secret sharing scheme which is linear over a sufficiently large field can be transformed into a strongly secure scheme with the same access structure preserving the information ratio. Since our method only requires linearity, our strongly secure schemes can realize arbitrary access structures and achieve smaller information ratio than the previous schemes.

秘密共享方案是一种加密技术，可以通过将秘密分成多个部分来保护其免遭丢失和泄漏。斜线秘密共享方案可以通过允许有关秘密的部分信息（由几个子秘密组成）泄漏出去来提高信息比率的效率。引入了强安全性概念来控制未经授权的集合可以获得的子秘密的每个子集上的信息量。然而，已经提出了很少的方法来构造用于通用访问结构的强安全方案。此外，所有现有方法都需要强有力的假设，这会导致效率降低和访问结构的限制。在本文中，我们表明，在足够大的范围内线性的任何斜坡秘密共享方案都可以转换为具有相同访问结构并保留信息比率的强安全方案。由于我们的方法仅需要线性，因此与以前的方案相比，我们的高度安全的方案可以实现任意访问结构并实现较小的信息比率。