Threshold secret sharing is a fundamental building block in information security to provide secrecy and robustness services for various cryptographic protocols. According to the definition of (t, n) threshold secret sharing, the secret is divided into n shares, such that any t or more than t of these shares allow the secret to be reconstructed; but less than t shares reveal no information of the secret. In other words, this definition only considers protection of the secret from colluded insiders but not outsiders. In this paper, we propose an extended secret sharing scheme, called secret sharing with secure secret reconstruction, in which the secret can be protected in the reconstruction phase from both attacks of insiders and outsiders. In traditional secret sharing schemes, when more than t shares are presented in the secret reconstruction, outsiders only need to intercept t shares to recover the secret. But in our proposed basic scheme, outsiders need to intercept all the released shares to recover the secret. Obviously, requiring more shares in the reconstruction contributes to security enhancement for this process. The limitation of this basic scheme is that it cannot prevent outsiders from learning the secret if they intercept all the released shares. To address this issue, we further extend the basic scheme so that the reconstructed secret is only accessible to shareholders, but not to outsiders. To the best of our knowledge, our extended scheme is the first secret sharing scheme that satisfies this property with information theoretical security.

阈值秘密共享是信息安全的基本组成部分，可为各种加密协议提供保密性和鲁棒性服务。根据（定义吨，  Ñ）阈值秘密共享，秘密分为Ñ股，使得任何吨或以上吨 这些股允许重构的秘密; 但少于t股则没有透露任何秘密信息。换句话说，此定义仅考虑保护机密免受串谋内部人员的侵害，而不考虑外部人员。在本文中，我们提出了一种扩展的秘密共享方案，称为带有安全秘密重构的秘密共享，其中可以在重建阶段保护机密不受内部人和外部人的攻击。在传统的秘密共享方案中，当秘密重建中出现t个以上的份额时，外部人只需要拦截t股份追回秘密。但是在我们提出的基本方案中，外部人员需要拦截所有已发行的股份以恢复秘密。显然，在重建中需要更多份额有助于此过程的安全性增强。此基本方案的局限性在于，如果外部人拦截所有已释放的份额，它就无法阻止外部人学习秘密。为了解决这个问题，我们进一步扩展了基本方案，以使重建的秘密仅对股东开放，而对外部人则不开放。据我们所知，我们的扩展方案是第一个通过信息理论安全性满足此特性的秘密共享方案。