A comprehensive review on collision-resistant hash functions on lattices

Nimish Mishra, SK Hafizul Islam, Sherali Zeadally

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Hash functions have always attracted a lot of attention in modern cryptography because of their hard to invert nature. However, all previous constructions of cryptographic primitives face the threat of being broken by the recent advancements in quantum technology. The focus has thus shifted to developing cryptographic primitives on mathematical structures such as lattices that are intractable by quantum algorithms. We review the computational problems defined on lattices and their respective hardness and discuss constructions of hash function families based on both integer and ideal lattices whose security depends on these computational problems on lattices. We provide a comparative analysis of the theoretical security and concrete instantiations claimed by the different hash function families. Finally, we review techniques used in the reductions for the security proofs of constructions of different hash function families.

Original languageEnglish
Article number102782
JournalJournal of Information Security and Applications
StatePublished - May 2021

Bibliographical note

Publisher Copyright:
© 2021 Elsevier Ltd


  • Closest vector problem
  • Hash function
  • Lattice
  • Shortest vector problem
  • Worst-case hardness assumption

ASJC Scopus subject areas

  • Software
  • Safety, Risk, Reliability and Quality
  • Computer Networks and Communications


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