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 $t$ 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 $F_q$ 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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2021/726}},
      url = {https://eprint.iacr.org/2021/726}
}
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