Tightness Subtleties for Multi-user PKE Notions

Hans Heum; Martijn Stam

Paper 2022/855

Tightness Subtleties for Multi-user PKE Notions

Hans Heum

, Simula UiB

Martijn Stam

, Simula UiB

Abstract

Public key encryption schemes are increasingly being studied concretely, with an emphasis on tight bounds even in a multi-user setting. Here, two types of formalization have emerged, one with a single challenge bit and one with multiple challenge bits. Another modelling choice is whether to allow key corruptions or not. How tightly the various notions relate to each other has hitherto not been studied in detail. We show that in the absence of corruptions, single-bit left-or-right indistinguishability is the preferred notion, as it tightly implies the other (corruption-less) notions. However, in the presence of corruptions, this implication no longer holds; we suggest the use of a more general notion that tightly implies both existing options. Furthermore, for completeness we study how the relationship between left-or-right versus real-or-random evolves in the multi-user PKE setting.

Note: Full version

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. IMA Coding and Cryptography Conference 2021
DOI: 10.1007/978-3-030-92641-0_5
Keywords: Indistinguishability Public Key Encryption Multi-User Security Adaptive Corruptions
Contact author(s): hansh @ simula no
martijn @ simula no
History: 2023-09-08: last of 2 revisions; 2022-06-28: received; See all versions
Short URL: https://ia.cr/2022/855
License: CC BY-NC-ND

BibTeX

@misc{cryptoeprint:2022/855,
      author = {Hans Heum and Martijn Stam},
      title = {Tightness Subtleties for Multi-user {PKE} Notions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2022/855},
      year = {2022},
      doi = {10.1007/978-3-030-92641-0_5},
      url = {https://eprint.iacr.org/2022/855}
}