Threshold-Secure Coding with Shared Key
Nasser Aldaghri, Hessam Mahdavifar

TL;DR
This paper introduces a threshold-secure coding framework using shared keys and linear codes, including Reed-Muller codes, to ensure security and reliability over noiseless and noisy channels with efficient implementation.
Contribution
It presents a novel threshold-secure coding scheme based on Reed-Muller codes, extending to noisy channels, with a comprehensive framework for construction and analysis.
Findings
Threshold-secure codes prevent eavesdroppers from gaining key or input information.
Efficient quasi-linear time encoding and decoding are achievable with Reed-Muller codes.
The schemes are adaptable for different key lengths and channel conditions.
Abstract
Cryptographic protocols are often implemented at upper layers of communication networks, while error-correcting codes are employed at the physical layer. In this paper, we consider utilizing readily-available physical layer functions, such as encoders and decoders, together with shared keys to provide a threshold-type security scheme. To this end, we first consider a scenario where the effect of the physical layer is omitted and all the channels between the involved parties are assumed to be noiseless. We introduce a model for threshold-secure coding, where the legitimate parties communicate using a shared key such that an eavesdropper does not get any information, in an information-theoretic sense, about the key as well as about any subset of the input symbols of size up to a certain threshold. Then, a framework is provided for constructing threshold-secure codes from linear block…
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