English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

All-or-nothing transforms (AONTs) were originally defined by Rivest asbijections from $s$ input blocks to $s$ output blocks such that no informationcan be obtained about any input block in the absence of any output block.Numerous generalizations and extensions of all-or-nothing transforms have beendiscussed in recent years, many of which are motivated by diverse applicationsin cryptography, information security, secure distributed storage, etc. Inparticular, $t$-AONTs, in which no information can be obtained about any $t$input blocks in the absence of any $t$ output blocks, have receivedconsiderable study.  In this paper, we study three generalizations of AONTs that are motivated byapplications due to Pham et al. and Oliveira et al. We term thesegeneralizations rectangular, range, and restricted AONTs. Briefly, in arectangular AONT, the number of outputs is greater than the number of inputs. Arange AONT satisfies the $t$-AONT property for a range of consecutive values of$t$. Finally, in a restricted AONT, the unknown outputs are assumed to occurwithin a specified set of "secure" output blocks. We study existence andnon-existence and provide examples and constructions for these generalizations.We also demonstrate interesting connections with combinatorial structures suchas orthogonal arrays, split orthogonal arrays, MDS codes and differencematrices.

Rectangular, Range, and Restricted AONTs: Three Generalizations of All-or-Nothing Transforms