Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Attainable Unconditional Security for Shared-Key Cryptosystems

Fabrizio Biondi 1 Thomas Given-Wilson 1 Axel Legay 1
1 TAMIS - Threat Analysis and Mitigation for Information Security
IRISA-D4 - LANGAGE ET GÉNIE LOGICIEL, Inria Rennes – Bretagne Atlantique
Abstract : Preserving the privacy of private communication is a fundamental concern of computing addressed by encryption. Information-theoretic reasoning models unconditional security where the strength of the results does not depend on computational hardness or unproven results. Usually the information leaked on the message by the ciphertext is used to measure the privacy of a communication, with perfect secrecy when the leakage is zero. However this is hard to achieve in practice. An alternative measure is the equivocation, intuitively the average number of message/key pairs that could have produced a given ciphertext. We show a theoretical bound on equivocation called max-equivocation and show that this generalizes perfect secrecy when achievable, and provides an alternative measure when perfect secrecy is not. We derive bounds for max-equivocation for symmetric encoder functions and show that max-equivocation is achievable when the entropy of the ciphertext is minimized. We show that max-equivocation easily accounts for key re-use scenarios, and that large keys relative to the message perform very poorly under equivocation. We study encoders under this new perspective, deriving results on their achievable maximal equivocation and showing that some popular approaches such as Latin squares are not optimal. We show how unicity attacks can be naturally modeled, and how breaking encoder symmetry improves equivocation. We present some algorithms for generating encryption functions that are practical and achieve 90-95% of the theoretical best, improving with larger message spaces.
Complete list of metadata

Cited literature [13 references]  Display  Hide  Download

https://hal.inria.fr/hal-01233185
Contributor : Fabrizio Biondi <>
Submitted on : Thursday, April 21, 2016 - 12:00:42 PM
Last modification on : Thursday, January 7, 2021 - 4:25:47 PM
Long-term archiving on: : Friday, July 22, 2016 - 12:18:18 PM

File

main.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01233185, version 2

Citation

Fabrizio Biondi, Thomas Given-Wilson, Axel Legay. Attainable Unconditional Security for Shared-Key Cryptosystems. 2016. ⟨hal-01233185v2⟩

Share

Metrics

Record views

617

Files downloads

263