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A generalized quantum relative entropy
doi: 10.3934/amc.2020027
Group signature from lattices preserving forward security in dynamic setting
Meenakshi Kansal , , Ratna Dutta and Sourav Mukhopadhyay
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur-721302, India
* Corresponding author: Meenakshi Kansal
Received October 2018 Revised March 2019 Published September 2019
Figure(1) / Table(1)
We propose the first lattice-based dynamic group signature scheme achieving forward security. Our scheme is proven to be secure against framing attack, misidentification attack and preserves anonymity under the learning with errors (${\mathsf{LWE}}$) and short integer solution (${\mathsf{SIS}}$) assumptions in the random oracle model. More interestingly, our setting allows the group manager to generate distinct certificates to distinct users which can be updated by the users themselves without any interaction with the group manager. Furthermore, our scheme is dynamic where signing key of a user is not fixed during the setup and is issued only at the joining time of the user.
Keywords: Lattice based cryptography, dynamic group signature, forward security, anonymity, traceability.
Mathematics Subject Classification: 94A60.
Citation: Meenakshi Kansal, Ratna Dutta, Sourav Mukhopadhyay. Group signature from lattices preserving forward security in dynamic setting. Advances in Mathematics of Communications, doi: 10.3934/amc.2020027
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Figure 1. Node Labeling
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Table 1. Comparative summary of lattice based group signature schemes
Scheme Forward secure Dynamic Signature size Public key size Certificate size Signer's SK size
[8] No No $ N\cdot \tilde{\mathcal{O}}(n^2) $ $ N\cdot \tilde{\mathcal{O}}(n^2) $ - $ \tilde{\mathcal{O}}(n^2) $
[10] No No $ \log N \cdot \tilde{\mathcal{O}}(n) $ $ \log N \cdot \tilde{\mathcal{O}}(n^2) $ - $ \tilde{\mathcal{O}}(n^2) $
[14] No No $ \log N \cdot \tilde{\mathcal{O}}(n) $ $ \log N \cdot \tilde{\mathcal{O}}(n^2) $ - $ \tilde{\mathcal{O}}(n) $
[11] No Yes $ \log N \cdot \tilde{\mathcal{O}}(n) $ $ \log N \cdot \tilde{\mathcal{O}}(n^2) $ $ \log N \cdot \mathcal{O}(n) $ $ \tilde{\mathcal{O}}(n) $
[15] Yes No $ \log N \cdot \tilde{\mathcal{O}}(n) $ $ \log N \cdot \tilde{\mathcal{O}}(n^2) $ - $ \log N \; \tilde{\mathcal{O}}(n^2) $
Ours Yes Yes $ \log N\; \tilde{\mathcal{O}}(n^3) $ $ \log N \cdot \tilde{\mathcal{O}}(n^2) $ $ \log N \; \tilde{\mathcal{O}}(n^2) $ $ \tilde{\mathcal{O}}(n) $
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Meenakshi Kansal Ratna Dutta Sourav Mukhopadhyay