Asymmetric All-or-nothing Transforms

In this paper, we initiate a study of asymmetric all-or-nothing transforms (or asymmetric AONTs). A (symmetric) \(t\)-all-or-nothing transform is a bijective mapping defined on the set of \(s\)-tuples over a specified finite alphabet. It is required that knowledge of all but \(t\) outputs leaves any...

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Bibliographic Details
Published inarXiv.org
Main Authors Navid Nasr Esfahani, Stinson, Douglas R
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 31.05.2021
Subjects
Alphabets
Asymmetry
Cryptography
Fields (mathematics)
Linear transformations
Mapping
Parameters
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Summary:In this paper, we initiate a study of asymmetric all-or-nothing transforms (or asymmetric AONTs). A (symmetric) \(t\)-all-or-nothing transform is a bijective mapping defined on the set of \(s\)-tuples over a specified finite alphabet. It is required that knowledge of all but \(t\) outputs leaves any \(t\) inputs completely undetermined. There have been numerous papers developing the theory of AONTs as well as presenting various applications of AONTs in cryptography and information security. In this paper, we replace the parameter \(t\) by two parameters \(t_o\) and \(t_i\), where \(t_i \leq t_o\). The requirement is that knowledge of all but \(t_o\) outputs leaves any \(t_i\) inputs completely undetermined. When \(t_i < t_o\), we refer to the AONT as asymmetric. We give several constructions and bounds for various classes of asymmetric AONTs, especially those with \(t_i = 1\) or \(t_i = 2\). We pay particular attention to linear transforms, where the alphabet is a finite field \(\mathbb{F}_q\) and the mapping is linear.
ISSN:2331-8422