دانلود رایگان مقاله ارتباطات قابل اعتماد و کاملا مخفی بیش از کانال تعمیم یافته Ozarow-Wyner

Abstract

In a typical secure communication system, messages undergo two different encodings: an error-correcting code is applied at the physical layer to ensure correct reception by the addressee (integrity), while at an upper protocol layer cryptography is leveraged to enforce secrecy with respect to eavesdroppers (confidentiality). All constructive solutions proposed so far to concurrently achieve both integrity and confidentiality at the physical layer, aim at meeting the secrecy capacity of the channel, i.e., at maximizing the rate of the code while guaranteeing an asymptotically small information leakage. In this paper, we propose a viable encoding scheme that, to the best of our knowledge, is the first one to guarantee both perfect secrecy (i.e., no information leakage) and reliable communication over the generalized Ozarow-Wyner’s wire-tap channel. To this end, we first introduce a metric called uncertainty rate that, similarly to the equivocation rate metric, captures the amount of information leaked by a coding scheme in the considered threat model, but it is simpler to apply in the context of linear codes. Based on this metric, we provide an alternative and simpler proof of the known result that no linear error-correcting code alone can achieve perfect secrecy. Finally, we propose a constructive solution combining secret sharing and linear error-correcting codes, and we show that our solution provides the desired combination of reliable and perfectly secret communication. The provided solution, other than being supported by thorough analysis, is viable in practical communication systems.

6. Conclusion

In this paper, we focused on the Generalized Ozarow-Wyner’s wire-tap (GOW) channel model and, to the best of our knowledge, we are the first to provide constructive solutions that combine secret sharing and linear error-correcting codes to overcome the presence of transmission errors, while guaranteeing perfect security. We also introduced a security metric, called uncertainty rate, that specifies the equivocation rate in the context of linear errorcorrecting codes. This newly introduced metric, other than being instrumental to our proposal, also helped to state, in a simple way, theoretical results concerning the implementation of ECC encoders in the GOW channel model that were already known for the traditional wire-tap channel model—yet, requiring a complex technical machinery. It is worth noticing that our work significantly deviates from the research trend in the area. In fact, most papers focus on the secrecy capacity, studying limiting behaviours of the model when the size of the message approaches infinity. Taking a different approach, we showed that reliable and perfectly secret communication is possible in practice, at the cost of a (slightly) lower communication rate. Moreover, we also provided a generic and constructive procedure for obtaining a secure wire-tap code from a linear encoder. While the proposed formalization and theoretical contributions stand on their own, they have also a wealth of practical applications, for instance in contexts where the amount of transmitted data is limited, or where key management and costly cryptographic algorithms are hard to implement—such as in many distributed and unattended application settings—or, finally, where perfect secrecy is at premium.