New efficient constructions of verifiable data streaming with accountability


Data streaming is widely used in various environments. Resource-limited devices outsource the processing and storage of massive numbers of sequential elements to cloud-based servers, and security protection is of primary importance for the outsourced streams. The streaming authenticated data structure schemes and verifiable data streaming schemes are introduced to provide data owners and verifiers with the ability to verify streaming elements. However, due to their enormous numbers of key parameters, expensive updating overheads, signature revocation, and other security and application problems, few of the existing schemes are feasible when massive numbers of streaming elements are involved and allowed to be updated. In this paper, we define and construct a new primitive, namely, dimension-increasing vector commitment (DIVC). Then, we present the definition of constant verifiable data streaming (CVDS), which is an extension of the original verifiable data streaming (VDS) scheme. Moreover, with the proposed DIVC scheme, which is based on the CDH assumption in bilinear pairings, we construct two concrete CVDS schemes, namely, the probabilistic verifiability CVDS (P-CVDS) scheme and the deterministic verifiability CVDS (D-CVDS) scheme, by respectively employing the counting Bloom filter and a dynamic accumulator, which is based on the q-SDH assumption in bilinear pairings. The analyses prove that both the P-CVDS and D-CVDS schemes satisfy the security requirements that are formulated in the CVDS definition. Finally, the efficiency and performance evaluation demonstrate that the proposed schemes are feasible in practical applications.

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  1. 1.

    When we want to refer to the cell commitment value of a completed cell, for simplicity, in this context, we may employ any index that falls into the same cell, rather than only using the last index. In other words, for a completed cell, only the cell commitment value and its signature are stored in the server.

  2. 2.

    The purpose of splitting the proof is to support the security requirement of accountability; the core idea comes from the basic concept of verifiable outsourcing computation, which can be found in related works, such as [37, 38]. To reduce the client’s workload, the client proof πci can be released by a trusted agent or proxy instead of the client. In addition, in data streaming environments, since the client is always online until the data streaming has finished, there is no need to distinguish between when the client is online or offline in related algorithms.

  3. 3.

    In this scheme, n is equal to the maximum number of cells in the data stream, which means there could be n × s stream elements.

  4. 4.

    According to the characteristics of the CBF scheme, if this step of verification is not passed, the final result of the CVDS.Verify() algorithm cannot be passed; however, if this verification step is passed, the final result could be correct or not. That is the reason why we say that this SVDS scheme is probabilistically verifiable.

  5. 5.

    The proof of commitment verification can be found in [13, 25] and other related works.

  6. 6.

    These parameters are mainly the security-related parameters, such as the security parameter in the setup algorithm of a verifiable data streaming scheme, the security parameter of an accumulator scheme, and the upper bound of element number within one Bloom filter.


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This work is supported by the National Natural Science Foundation of China (no. 61572382), Key Project of Natural Science Basic Research Plan in Shaanxi Province of China (no. 2016JZ021), China 111 Project (no. B16037), Guangxi Cooperative Innovation Center of cloud computing and Big Data (no. YD17X07), and Guangxi Colleges and Universities Key Laboratory of cloud computing and complex systems (no. YF17103).

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Correspondence to Zhiwei Zhang.

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Zhang, Z., Chen, X., Ma, J. et al. New efficient constructions of verifiable data streaming with accountability. Ann. Telecommun. 74, 483–499 (2019).

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  • Verifiable data streaming
  • Vector commitment
  • Counting Bloom filter
  • Dynamic accumulator
  • Cloud computing