Crooked indifferentiability of enveloped XOR revisited

Rishiraj Bhattacharyya*, Mridul Nandi, Anik Raychaudhuri

*Corresponding author for this work

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

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In CRYPTO 2018, Russell, Tang, Yung and Zhou (RTYZ) introduced the notion of crooked indifferentiability to analyze the security of a hash function when the underlying primitive is subverted. They showed that the n-bit to n-bit function implemented using enveloped XOR construction (EXor) with 3 n+ 1 many n-bit functions and 3 n2 -bit random initial vectors can be proven secure asymptotically in the crooked indifferentiability setting. We identify several major issues and gaps in the proof by RTYZ, We argue that their proof can achieve security only in a restricted setting. We present a new proof of crooked indifferentiability where the adversary can evaluate queries related to multiple messages. Our technique can handle function-dependent subversion.

Original languageEnglish
Title of host publicationProgress in Cryptology – INDOCRYPT 2021
Subtitle of host publication22nd International Conference on Cryptology in India, Jaipur, India, December 12–15, 2021, Proceedings
EditorsAvishek Adhikari, Ralf Küsters, Bart Preneel
Number of pages20
ISBN (Electronic)9783030925185
ISBN (Print)9783030925178
Publication statusPublished - 9 Dec 2021
Event22nd International Conference on Cryptology in India, INDOCRYPT 2021 - Jaipur, India
Duration: 12 Dec 202115 Dec 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13143 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference22nd International Conference on Cryptology in India, INDOCRYPT 2021

Bibliographical note

Publisher Copyright:
© 2021, Springer Nature Switzerland AG.


  • Crooked indifferentiability
  • Enveloped XOR Hash
  • Simulator
  • Subverted random oracle

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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