Secret sharing (SS) schemes have been widely used in secure computer communications systems. Recently, a new type of SS scheme, called the secure secret reconstruction scheme (SSRS), was proposed, which ensures that the secret can only be recovered by participants who present valid shares. In other words, if any outside adversary participated in the secret reconstruction without knowing any valid share, the secret cannot be recovered by anyone including the adversary. However, the proposed SSRS can only prevent an active attacker from obtaining the recovered secret, but cannot prevent a passive attacker from obtaining the secret since exchange information among participants is unprotected. In this paper, based on bivariate polynomials, we propose a novel design for the SSRS that can prevent both active and passive attackers. Furthermore, we propose a verification scheme which can verify all shares at once, i.e., it allows all shareholders to efficiently verify that their shares obtained from the dealer are generated consistently without revealing their shares and the secret. The proposed scheme is really attractive for efficient and secure secret reconstruction in communications systems.

中文翻译：

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基于对称双变量多项式的具有可验证份额的新型高效安全秘密重构方案（SSRS）

秘密共享（SS）方案已广泛用于安全的计算机通信系统中。最近，提出了一种新型的SS方案，称为安全秘密重建方案（SSRS），该方案可确保只有提供有效份额的参与者才能恢复该秘密。换句话说，如果任何外部对手在不知道任何有效份额的情况下参与了秘密重构，那么秘密的任何人都无法恢复该秘密。然而，由于参与者之间的交换信息不受保护，因此所提出的SSRS只能阻止主动攻击者获得恢复的秘密，而不能阻止被动攻击者获得秘密。在本文中，基于双变量多项式，我们为SSRS提出了一种新颖的设计，它可以防止主动和被动攻击者。此外，我们提出了一种可以一次验证所有股份的验证方案，即，它允许所有股东有效地验证从交易商那里获得的股份是一致产生的，而无需透露其股份和秘密。所提出的方案对于通信系统中的有效和安全的秘密重建确实具有吸引力。