On the Security Properties of Combinatorial All-or-nothing Transforms

Yujie Gu, Sonata Akao, Navid Nasr Esfahani, Ying Miao, Kouichi Sakurai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

All-or-nothing transforms (AONT) were proposed by Rivest as a message preprocessing technique for encrypting data to protect against brute-force attacks, and have many applications in cryptography and information security. Later the unconditionally secure AONT and their combinatorial characterization were introduced by Stinson. Informally, a combinatorial AONT is an array with the unbiased requirements and its security properties in general depend on the prior probability distribution on the inputs s-tuples. Recently, it was shown by Esfahani and Stinson that a combinatorial AONT has perfect security provided that all the inputs s-tuples are equiprobable, and has weak security provided that all the inputs s-tuples are with non-zero probability. This paper aims to explore on the gap between perfect security and weak security for combinatorial (t, s, v)-AONTs. Concretely, we consider the typical scenario that all the s inputs take values independently (but not necessarily identically) and quantify the amount of information H(X|Y) about any t inputs X that is not revealed by any s-t outputs Y. In particular, we establish the general lower and upper bounds on H(X|Y) for combinatorial AONTs using information-theoretic techniques, and also show that the derived bounds can be attained in certain cases.

Original languageEnglish
Title of host publication2022 IEEE International Symposium on Information Theory, ISIT 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1447-1452
Number of pages6
ISBN (Electronic)9781665421591
DOIs
Publication statusPublished - 2022
Event2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland
Duration: Jun 26 2022Jul 1 2022

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2022-June
ISSN (Print)2157-8095

Conference

Conference2022 IEEE International Symposium on Information Theory, ISIT 2022
Country/TerritoryFinland
CityEspoo
Period6/26/227/1/22

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Information Systems
  • Modelling and Simulation
  • Applied Mathematics

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