Secure Erasure Codes With Partial Reconstructibility
| Autor: | Alex Sprintson, Hoang Dau, Chau Yuen, Wentu Song |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Channel code
Group (mathematics) business.industry 020206 networking & telecommunications Field (mathematics) Cryptography 02 engineering and technology Library and Information Sciences Electronic mail Computer Science Applications Combinatorics Symbol (programming) Scheme (mathematics) 0202 electrical engineering electronic engineering information engineering business Erasure code Information Systems Mathematics |
| Zdroj: | IEEE Transactions on Information Theory. 66:6809-6822 |
| ISSN: | 1557-9654 0018-9448 |
| Popis: | We design $p$ - reconstructible $\mu $ - secure $[n,k]$ erasure coding schemes $(0 \leq \mu , which encode $k-\mu $ information symbols into $n$ coded symbols and moreover, satisfy the $k$ -out-of- $n$ property and the following two properties: (P1) strongly $\mu $ - secure – an adversary that accesses at most $\mu $ coded symbols gains no information about the information symbols; (P2) $p$ - reconstructible – a legitimate user can reconstruct each predetermined group of $p$ information symbols by accessing a predetermined group of $\mu + p$ coded symbols. The scheme is perfectly $p$ - reconstructible $\mu $ - secure if apart from (P1)-(P2), it also satisfies the following additional property: (P3) weakly $(\mu +p-1)$ - secure – an adversary that accesses at most $\mu +p-1$ coded symbols cannot reconstruct any single information symbol. In contrast with most related work in the literature, our codes guarantee partial reconstructibility due to (P2): once the user accesses $p$ more coded symbols than the threshold $\mu $ , it can reconstruct a specific group of $p$ information symbols. We provide an explicit construction of $p$ -reconstructible $\mu $ -secure coding schemes for all $\mu $ and $p$ over any field of size at least $n+1$ . We also establish a randomized construction for perfectly $p$ -reconstructible $\mu $ -secure coding schemes for all $\mu $ and $p$ satisfying $k\geq 2(\mu +p)-1$ over any field of size at least $n+k+k^{3}/4$ . |
| Databáze: | OpenAIRE |
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