Sparse Regression Codes for Secret Key Agreement: Achieving Strong Secrecy and Near-Optimal Rates for Gaussian Sources
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915413666824192 |
|---|---|
| author | Athanasakos, Emmanouil M. Manjunath, Hariprasad |
| author_facet | Athanasakos, Emmanouil M. Manjunath, Hariprasad |
| contents | Secret key agreement from correlated physical layer observations is a cornerstone of information-theoretic security. This paper proposes and rigorously analyzes a complete, constructive protocol for secret key agreement from Gaussian sources using Sparse Regression Codes (SPARCs). Our protocol systematically leverages the known optimality of SPARCs for both rate-distortion and Wyner-Ziv (WZ) coding, facilitated by their inherent nested structure. The primary contribution of this work is a comprehensive end-to-end analysis demonstrating that the proposed scheme achieves near-optimal secret key rates with strong secrecy guarantees, as quantified by a vanishing variational distance. We explicitly characterize the gap to the optimal rate, revealing a fundamental trade-off between the key rate and the required public communication overhead, which is governed by a tunable quantization parameter. Furthermore, we uncover a non-trivial constrained optimization for this parameter, showing that practical constraints on the SPARC code parameters induce a peak in the achievable secret key rate. This work establishes SPARCs as a viable and theoretically sound framework for secure key generation, providing a compelling low-complexity alternative to existing schemes and offering new insights into the practical design of such protocols. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20157 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sparse Regression Codes for Secret Key Agreement: Achieving Strong Secrecy and Near-Optimal Rates for Gaussian Sources Athanasakos, Emmanouil M. Manjunath, Hariprasad Information Theory Probability Applications Secret key agreement from correlated physical layer observations is a cornerstone of information-theoretic security. This paper proposes and rigorously analyzes a complete, constructive protocol for secret key agreement from Gaussian sources using Sparse Regression Codes (SPARCs). Our protocol systematically leverages the known optimality of SPARCs for both rate-distortion and Wyner-Ziv (WZ) coding, facilitated by their inherent nested structure. The primary contribution of this work is a comprehensive end-to-end analysis demonstrating that the proposed scheme achieves near-optimal secret key rates with strong secrecy guarantees, as quantified by a vanishing variational distance. We explicitly characterize the gap to the optimal rate, revealing a fundamental trade-off between the key rate and the required public communication overhead, which is governed by a tunable quantization parameter. Furthermore, we uncover a non-trivial constrained optimization for this parameter, showing that practical constraints on the SPARC code parameters induce a peak in the achievable secret key rate. This work establishes SPARCs as a viable and theoretically sound framework for secure key generation, providing a compelling low-complexity alternative to existing schemes and offering new insights into the practical design of such protocols. |
| title | Sparse Regression Codes for Secret Key Agreement: Achieving Strong Secrecy and Near-Optimal Rates for Gaussian Sources |
| topic | Information Theory Probability Applications |
| url | https://arxiv.org/abs/2507.20157 |