Verifiable secret sharing (VSS) is one of the basic problems in the theory of distributed cryptography and has an important role in secure multiparty computation. In this case, it is tried to share a confidential data as secret, between multiple nodes in a distributed system, in the presence of an active adversary that can destroy some nodes, such that the secret can be reconstructed with the participation of certain size of honest nodes. A dynamic adversary can change its corrupted nodes among the protocol. So far, there is not a formal definition and there are no protocols of dynamic adversaries in VSS context. Also, another important question is, would there exist a protocol to share a secret with a static adversary with at most 1 broadcast round? In this paper, we provide a formal definition of the dynamic adversary. The simulation results prove the efficiency of the proposed protocol in terms of the runtime, the memory usage, and the number of message exchanges. We show that the change period of the dynamic adversary could not happen in less than 4 rounds in order to have a perfectly secure VSS, and then we establish a protocol to deal with this type of adversary. Also, we prove that the lower bound of broadcast complexity for the static adversary is (2,0)-broadcast rounds.

中文翻译：

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可验证秘密共享中的广播复杂性和自适应对手

可验证秘密共享（VSS）是分布式密码学理论中的基本问题之一，在安全的多方计算中具有重要作用。在这种情况下，尝试在存在可以破坏某些节点的活动对手的情况下，在分布式系统中的多个节点之间共享作为机密数据的机密数据，以便可以在一定大小的攻击者的参与下重建机密。诚实节点。动态对手可以在协议中更改其损坏的节点。到目前为止，在VSS上下文中还没有正式的定义，也没有动态对手的协议。另外，另一个重要的问题是，是否存在一种协议，可以与静态对手共享最多一个广播回合的秘密？在本文中，我们提供了动态对手的正式定义。仿真结果证明了所提协议在运行时，内存使用和消息交换数量方面的效率。我们展示了动态对手的更改期不可能少于4轮才能拥有一个完全安全的VSS，然后我们建立了一个协议来处理这种类型的对手。同样，我们证明了静态对手的广播复杂度下限是（2,0）-广播回合。