The identity-based homomorphic signature (IBHS) enables an untrusted server to run some computation over the outsourced data and derive a short signature, vouching for the correctness of the output of the computation, while greatly simplifying key management. To our knowledge, constructions of IBHS have been few and far between. However, the existing IBHS schemes, which either handle only linear functions or has a large public key parameter and satisfies only the artificial notion of selective security. In this work, we construct the first leveled adaptively secure identity-based fully homomorphic signature (IBFHS) schemes without additional public parameters, which can be used to sign many different datasets. Thereby positively answering the open question of constructing a leveled IBFHS scheme with short public parameters, proposed by Wang et al., (ISC, 2015, Springer). We achieve the stronger security and better parameters by using the trapdoor vanishing and vector encoding technique. In our scheme, the size of every evaluated signature depends only logarithmically on the size of the input dataset, and the complexity of verifying a signature for a computation can be amortized when verifying the same computation on many different datasets. Furthermore, we prove that our construction is strongly-unforgeable against adaptively chosen identity and message attacks under the small integer solution (SIS) assumption in standard lattices.
With the rapid development of informatization, an increasing number of industries and organizations outsource their data to cloud servers, to avoid the cost of local data management and to share data. For example, industrial Internet of things systems and mobile healthcare systems rely on cloud computing's powerful data storage and processing capabilities to address the storage, provision, and maintenance of massive amounts of industrial and medical data. One of the major challenges facing cloud-based storage environments is how to ensure the confidentiality and security of outsourced sensitive data. To mitigate these issues, He et al. and Ma et al. have recently independently proposed two certificateless public key searchable encryption schemes. In this paper, we analyze the security of these two schemes and show that the reduction proof of He et al.'s CLPAEKS scheme is incorrect, and that Ma et al.'s CLPEKS scheme is not secure against keyword guessing attacks. We then propose a channel-free certificateless searchable public key authenticated encryption (dCLPAEKS) scheme and prove that it is secure against inside keyword guessing attacks under the enhanced security model. Compared with other certificateless public key searchable encryption schemes, this scheme has higher security and comparable efficiency.
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