The edge authentication of graphs has been studied in the literature because graphs are one of the most widely used data organization structures. The majority of such schemes cannot be used to authenticate general directed graphs (GDGs); other schemes cannot be used for addressing either the issue of dynamic update or the issue of information leakage (such as the existence of nodes/edges and structural relationship of the graph). Also, all the existing schemes do not consider the forward security: if the signer’s secret key has been compromised, all previously generated signatures remain valid. This property provides high-level security protection for authentication schemes. To address these issues, in this work, we propose a forward-secure edge authentication scheme for GDGs. Observe that existing such schemes can only give a proof such that ‘there is an edge between nodes $u$ and $v$’. Our scheme, however, can directly give a proof such that ‘there is no edge between nodes $u$ and $v$’, which makes the function of edge authentication schemes more diverse. Moreover, our proposed scheme is proven to be secure against an adaptive chosen-message adversary in the random oracle model. To show its desirable performance, we analyze the computational costs of our scheme and compare it with other related schemes in terms of features.

中文翻译：

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图的前向安全边缘身份验证

由于图是最广泛使用的数据组织结构之一，因此在文献中已经研究了图的边缘认证。大多数此类方案不能用于验证通用有向图（GDG）；其他方案不能用于解决动态更新问题或信息泄漏问题（例如节点/边的存在和图的结构关系）。此外，所有现有方案都没有考虑前向安全性：如果签名者的密钥已被泄露，则所有先前生成的签名仍然有效。此属性为身份验证方案提供高级别的安全保护。为了解决这些问题，在这项工作中，我们提出了一种用于 GDG 的前向安全边缘认证方案。请注意，现有的此类方案只能提供“节点 $u$ 和 $v$ 之间存在边”的证明。然而，我们的方案可以直接给出“节点$u$和$v$之间没有边”的证明，这使得边认证方案的功能更加多样化。此外，我们提出的方案被证明在随机预言模型中对自适应选择消息对手是安全的。为了展示其理想的性能，我们分析了我们方案的计算成本，并在特征方面与其他相关方案进行了比较。我们提出的方案被证明在随机预言模型中对自适应选择消息对手是安全的。为了展示其理想的性能，我们分析了我们方案的计算成本，并在特征方面与其他相关方案进行了比较。我们提出的方案被证明在随机预言模型中对自适应选择消息对手是安全的。为了展示其理想的性能，我们分析了我们方案的计算成本，并在特征方面与其他相关方案进行了比较。