In a secret sharing scheme, a dealer, D, distributes shares of a secret, S among a set of n participants, such that only authorised subsets of these participants can reconstruct S, by pooling their shares. Unauthorised subsets should gain no information. An extensively researched area within this field is how to cope with participants who arbitrarily modify their shares (i.e. cheaters). A secret sharing scheme with cheating detection capabilities (SSCD) allows participants to detect cheating upon reconstruction time. The most common way of achieving this is to utilise an algebraic manipulation detection (AMD) code alongside a secret sharing scheme. The dealer essentially encodes S in an AMD code and distributes this code to participants. Participants then reconstruct the code and use this to detect cheating. The problem with this approach is that even if cheating is detected, the cheaters still get the secret. To overcome this problem, we propose a new protocol: outsourced SSCD (OSSCD). Our proposed protocol utilises the same techniques as SSCD; however, before the secret is reconstructed, we have participants distribute their shares among a set of special validation servers. These validation servers then perform a public computation to determine if cheating has occurred. They do this without reconstructing S. The result of this is that if cheating has occurred, the servers can halt the protocol, ensuring no one learns the secret. We present two efficient constructions of our proposed OSSCD protocol: one capable of detecting cheating with high probability and the other capable of tolerating many secrets simultaneously.

在秘密共享方案中，交易者D在n个参与者的集合中分配秘密S的份额，以使只有这些参与者的授权子集才能通过合并他们的份额来重建S。未经授权的子集不应获得任何信息。在该领域内，一个广泛研究的领域是如何应对任意修改其股份（即作弊者）的参与者。具有作弊检测功能（SSCD）的秘密共享方案允许参与者在重建时检测作弊。实现此目的的最常见方法是在秘密共享方案旁边使用代数操作检测（AMD）代码。发牌人本质上编码S在AMD代码中并将其分发给参与者。然后，参与者重新构建代码，并使用它来检测作弊行为。这种方法的问题在于，即使检测到作弊，作弊者仍会获得秘密。为了克服这个问题，我们提出了一个新的协议：外包SSCD（OSSCD）。我们提出的协议使用与SSCD相同的技术；但是，在重建秘密之前，我们让参与者在一组特殊的验证服务器之间分配了他们的份额。然后，这些验证服务器将执行公共计算，以确定是否发生了欺诈行为。他们这样做而无需重建S。这样的结果是，如果发生了欺诈行为，服务器可以停止该协议，从而确保没有人知道秘密。我们提出了我们提出的OSSCD协议的两种有效构造：一种能够以高概率检测到作弊，而另一种能够同时容忍许多秘密。