论文标题
在有恶意对手的情况下，沟通有效的秘密共享
Communication Efficient Secret Sharing in the Presence of Malicious Adversary
论文作者
论文摘要
考虑沟通有效的秘密共享问题。经销商希望与$ n $ party方共享一个秘密，以便任何$ k \ leq n $ parties都可以重建秘密，任何$ z <k $ partions afforpone neverpoping int and of股份都没有获得有关该秘密的信息。此外，与任何$ d $，$ k \ leq d \ leq n $联系的合法用户，通过阅读和下载所需的最低信息量来解码该秘密的当事方可以做到这一点。我们对沟通有效的秘密共享计划感兴趣，这些计划容忍恶意政党的存在会积极损害其股份以及交付给用户的数据。恶意政党关于秘密的知识仅限于他们获得的股份。我们表征了容量，即可以共享的秘密的最大大小。我们得出要阅读并传达合法用户所需的最低信息量，以将秘密从$ d $ partions（$ k \ leq d \ leq n $）解码。在此设置中，错误纠正的代码无法实现能力。我们构建实现容量并实现所有可能值$ d $的最低阅读和通信成本的代码。我们的代码基于楼梯代码，以前引入了用于通信有效秘密共享的阶梯代码，以及使用用于分布式数据存储和网络编码设置的成对哈希方案，以检测有限的知识对手插入的错误。
Consider the communication efficient secret sharing problem. A dealer wants to share a secret with $n$ parties such that any $k\leq n$ parties can reconstruct the secret and any $z<k$ parties eavesdropping on their shares obtain no information about the secret. In addition, a legitimate user contacting any $d$, $k\leq d \leq n$, parties to decode the secret can do so by reading and downloading the minimum amount of information needed. We are interested in communication efficient secret sharing schemes that tolerate the presence of malicious parties actively corrupting their shares and the data delivered to the users. The knowledge of the malicious parties about the secret is restricted to the shares they obtain. We characterize the capacity, i.e. maximum size of the secret that can be shared. We derive the minimum amount of information needed to to be read and communicated to a legitimate user to decode the secret from $d$ parties, $k\leq d \leq n$. Error-correcting codes do not achieve capacity in this setting. We construct codes that achieve capacity and achieve minimum read and communication costs for all possible values of $d$. Our codes are based on Staircase codes, previously introduced for communication efficient secret sharing, and on the use of a pairwise hashing scheme used in distributed data storage and network coding settings to detect errors inserted by a limited knowledge adversary.
