Robust Secure Authentication and Data Storage with Perfect Secrecy
Abstract
:1. Introduction
2. Authentication Model
3. Various Definitions of Achievability
4. Capacity Regions for the Authentication Model
5. Compound Authentication Model
6. Achievability for the Compound Model
7. Capacity Regions for the Compound Authentication Model
- We consider a partition of the set of all sets in subsets. Thus, we denote the sets by , , indicating to which subset they belong. We denote the set of indices m corresponding to by . For each , we have
- Each consists of sequences of the same type.
- It holds that
- For each , one can define pairs of mappings that are compound -codes, , for the channels , for all in the following way. Define an (arbitrary) bijective mapping and an appropriate mapping . Then, is such a code. This means
- We define and as follows. The system gets a sequence . It checks if , , for an (We can choose small enough and n large enough such that the are disjoint). If this is true for , the channel is used n times to generate from . For , the system looks in for . If the system chooses for m the index of the subset containing . If it chooses an arbitrary . In addition, if , it chooses an arbitrary . For , the system looks in for . If , it considers the compound -code corresponding to the subset containing . If
- We define as follows. The system gets a sequence and m. It decodes using the code corresponding to . Then, is used on the result. The result is if it differs from . Otherwise, an arbitrary is chosen.
- We define the following events:
- We define
- For the secret-key rate, we have
- Finally, we analyse the privacy-leakage rate. We have
8. Secure Storage
9. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A. Proof of Theorem 4
Appendix B. Equivalence of Rate Regions
Appendix C. Modifying Markov Chains
- We have
- We have for all from . Summing both sides over all , we get Implication (A11).
- We have
- We have
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Baur, S.; Boche, H. Robust Secure Authentication and Data Storage with Perfect Secrecy. Cryptography 2018, 2, 8. https://doi.org/10.3390/cryptography2020008
Baur S, Boche H. Robust Secure Authentication and Data Storage with Perfect Secrecy. Cryptography. 2018; 2(2):8. https://doi.org/10.3390/cryptography2020008
Chicago/Turabian StyleBaur, Sebastian, and Holger Boche. 2018. "Robust Secure Authentication and Data Storage with Perfect Secrecy" Cryptography 2, no. 2: 8. https://doi.org/10.3390/cryptography2020008