Abstract
Fault-tolerant aggregate signature (FT-AS) is a special type of aggregate signature that is equipped with the functionality for tracing signers who generated invalid signatures in the case an aggregate signature is detected as invalid. In existing FT-AS schemes (whose tracing functionality requires multi-rounds), a verifier needs to send a feedback to an aggregator for efficiently tracing the invalid signer(s). However, in practice, if this feedback is not responded to the aggregator in a sufficiently fast and timely manner, the tracing process will fail. Therefore, it is important to estimate whether this feedback can be responded and received in time on a real system.
In this work, we measure the total processing time required for the feedback by implementing an existing FT-AS scheme, and evaluate whether the scheme works without problems in real systems. Our experimental results show that the time required for the feedback is 605.3 ms for a typical parameter setting, which indicates that if the acceptable feedback time is significantly larger than a few hundred ms, the existing FT-AS scheme would effectively work in such systems. However, there are situations where such feedback time is not acceptable, in which case the existing FT-AS scheme cannot be used. Therefore, we further propose a novel FT-AS scheme that does not require any feedback. We also implement our new scheme and show that a feedback in this scheme is completely eliminated but the size of its aggregate signature (affecting the communication cost from the aggregator to the verifier) is 144.9 times larger than that of the existing FT-AS scheme (with feedbacks) for a typical parameter setting, and thus has a trade-off between the feedback waiting time and the communication cost from the verifier to the aggregator with the existing FT-AS scheme.
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Notes
- 1.
In this paper, we mainly focus on signers that probabilistically generate invalid signatures. However, we can think of them as corrupted by a malicious party.
- 2.
In general, aggregate signatures can aggregate multiple signatures even if they are generated under the same key.
- 3.
It takes 0.679 ms per group operation and 286 ms per pairing operation in our setting.
- 4.
In the tracing algorithm of AS-FT-2, when the verifier finds an invalid aggregate signature, it outputs a feedback and the rest of signatures are not verified.
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Acknowledgement
This work was partially supported by the Cabinet Office (CAO), Cross-ministerial Strategic Innovation Promotion Program (SIP), “Cyber Physical Security for IoT Society", JPNP18015 (funding agency: NEDO).
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Ishii, R. et al. (2022). Constraints and Evaluations on Signature Transmission Interval for Aggregate Signatures with Interactive Tracing Functionality. In: Li, W., Furnell, S., Meng, W. (eds) Attacks and Defenses for the Internet-of-Things. ADIoT 2022. Lecture Notes in Computer Science, vol 13745. Springer, Cham. https://doi.org/10.1007/978-3-031-21311-3_3
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