Abstract
Tightening the security reduction of a cryptosystem involves reducing the advantage of an adversary breaking the cryptosystem to a security assumption as closely as possible. Tighter security on a cryptosystem shows a clearer picture of its security, allowing for a more optimal security parameter at a certain level. In this work, we propose techniques to tighten the security of identity-based identification (IBI) schemes and demonstrate promising new results compared to existing reduction bounds. We show two distinct transformations for tightening security against concurrent attackers via the OR-proof technique of Fujioka et al. to lower security reduction loss. Our proposed techniques produce tighter security guarantees for as low as only a one-bit loss bound, hence the name: OrBit.
Supported by the Ministry of Higher Education of Malaysia through the Fundamental Research Grant Scheme (FRGS/1/2019/ICT04/MMU/02/5.) and the Multimedia University fund.
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Notes
- 1.
The signature was already queried to the forgery oracle, thus cannot be used as a forgery.
- 2.
- 3.
The exposure of user-bit b to the active adversary enables it to always output a bit \(b^* = b\) causing the security reduction of [9] to fail. The use of OR-proof fixes the problem and we achieve the same security bound and assumption as theirs.
- 4.
This is also the reason why R was stored for each user. If R was randomly generated for different PROV queries, CV would be able to distinguish b by running PROV query on the same ID twice and checking \(W_0\) and \(W_1\).
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Acknowledgements
The authors would like to thank the anonymous reviewers for their helpful and critical feedback in the preliminary version of this paper. In addition, the authors acknowledge the Fundamental Research Grant Scheme awarded by the Ministry of Higher Education of Malaysia (FRGS/1/2019/ICT04/MMU/02/5) and the Multimedia University fund.
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Chia, J., Chin, JJ., Yip, SC. (2021). OrBit: OR-Proof Identity-Based Identification with Tight Security for (as Low As) 1-Bit Loss. In: Huang, Q., Yu, Y. (eds) Provable and Practical Security. ProvSec 2021. Lecture Notes in Computer Science(), vol 13059. Springer, Cham. https://doi.org/10.1007/978-3-030-90402-9_7
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