Asymmetric All-or-nothing Transforms

Navid Nasr Esfahani; Douglas R.  Stinson

Paper 2021/726

Asymmetric All-or-nothing Transforms

Navid Nasr Esfahani and Douglas R. Stinson

Abstract

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 by two parameters and , where . The requirement is that knowledge of all but outputs leaves any inputs completely undetermined. When , we refer to the AONT as asymmetric. We give several constructions and bounds for various classes of asymmetric AONTs, especially those with or . We pay particular attention to linear transforms, where the alphabet is a finite field and the mapping is linear.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: all-or-nothing transform
Contact author(s): dstinson @ uwaterloo ca
navid nasresfahani @ uwaterloo ca
History: 2021-06-02: received
Short URL: https://ia.cr/2021/726
License: CC BY

BibTeX

@misc{cryptoeprint:2021/726,
      author = {Navid Nasr Esfahani and Douglas R.  Stinson},
      title = {Asymmetric All-or-nothing Transforms},
      howpublished = {Cryptology {ePrint} Archive, Paper 2021/726},
      year = {2021},
      url = {https://eprint.iacr.org/2021/726}
}