Visible to the public Reliable and Secure Multishot Network Coding using Linearized Reed-Solomon Codes

TitleReliable and Secure Multishot Network Coding using Linearized Reed-Solomon Codes
Publication TypeConference Paper
Year of Publication2018
AuthorsMartínez-Peñas, Umberto, Kschischang, Frank R.
Conference Name2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Keywordscoding scheme, composability, computational complexity, cyber physical systems, Decoding, encoding, error correction codes, inject erroneous packets, Knowledge engineering, linear codes, linear network code, linearized Reed-Solomon codes, multishot network coding, network coding, network error-correction, Network topology, Predictive Metrics, pubcrawl, random codes, Reed-Solomon codes, reliability, reliable multishot network coding, Resiliency, secure multishot network coding, sum-rank metric, sum-subspace codes, telecommunication network topology, telecommunication security, unbounded computational resources, wire-tap channel, worst-case adversarial setting, zero-error communication
AbstractMultishot network coding is considered in a worst-case adversarial setting in which an omniscient adversary with unbounded computational resources may inject erroneous packets in up to t links, erase up to ρ packets, and wire-tap up to μ links, all throughout ℓ shots of a (random) linearly-coded network. Assuming no knowledge of the underlying linear network code (in particular, the network topology and underlying linear code may change with time), a coding scheme achieving zero-error communication and perfect secrecy is obtained based on linearized Reed-Solomon codes. The scheme achieves the maximum possible secret message size of ℓn'-2t-ρ-μ packets, where n' is the number of outgoing links at the source, for any packet length m ≥ n' (largest possible range), with only the restriction that ℓ\textbackslashtextless;q (size of the base field). By lifting this construction, coding schemes for non-coherent communication are obtained with information rates close to optimal for practical instances. A Welch-Berlekamp sum-rank decoding algorithm for linearized Reed-Solomon codes is provided, having quadratic complexity in the total length n = ℓn', and which can be adapted to handle not only errors, but also erasures, wire-tap observations and non-coherent communication.
Citation Keymartinez-penas_reliable_2018