Paper 2024/993

Limits on the Power of Prime-Order Groups: Separating Q-Type from Static Assumptions

George Lu, The University of Texas at Austin
Mark Zhandry, NTT Research
Abstract

Subgroup decision techniques on cryptographic groups and pairings have been critical for numerous applications. Originally conceived in the composite-order setting, there is a large body of work showing how to instantiate subgroup decision techniques in the prime-order setting as well. In this work, we demonstrate the first barrier to this research program, by demonstrating an important setting where composite-order techniques cannot be replicated in the prime-order setting. In particular, we focus on the case of $q$-type assumptions, which are ubiquitous in group- and pairing-based cryptography, but unfortunately are less desirable than the more well-understood static assumptions. Subgroup decision techniques have had great success in removing $q$-type assumptions, even allowing $q$-type assumptions to be generically based on static assumptions on composite-order groups. Our main result shows that the same likely does not hold in the prime order setting. Namely, we show that a large class of $q$-type assumptions, including the security definition of a number of cryptosystems, cannot be proven secure in a black box way from any static assumption.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published by the IACR in CRYPTO 2024
Keywords
generic group model
Contact author(s)
gclu @ cs utexas edu
mzhandry @ gmail com
History
2024-06-20: approved
2024-06-19: received
See all versions
Short URL
https://ia.cr/2024/993
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2024/993,
      author = {George Lu and Mark Zhandry},
      title = {Limits on the Power of Prime-Order Groups: Separating Q-Type from Static Assumptions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/993},
      year = {2024},
      url = {https://eprint.iacr.org/2024/993}
}
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