### An Analysis of the Algebraic Group Model

Jonathan Katz, Cong Zhang, and Hong-Sheng Zhou

##### Abstract

The algebraic group model (AGM), proposed by Fuchsbauer, Kiltz and Loss (CRYPTO 2018) has received huge attention. One of the most appealing properties of the AGM, is that, the hardness of security games in the generic group model (GGM) can be transferred via a generic reduction in the AGM. More concretely, for any two security games, G and H, if there exists a generic reduction from H to G in the AGM, and H is hard in the GGM, then G is also hard in the GGM. In this work, we analyze the relationship between the AGM and Shoup’s GGM (Eurocrypt 1997) and give evidence that: • hardness of security games in Shoup’s GGM cannot be transferred via a generic reduction in the AGM; • the AGM and Shoup’s GGM are incomparable.

Note: We add a subsection 1.3 on page 5, providing comparison to a concurrent and independent result by Mark Zhandry (eprint.iacr.org/2022/226), as well as presenting additional discussions.

Available format(s)
Category
Foundations
Publication info
Preprint. Minor revision.
Contact author(s)
hszhou @ vcu edu
congresearch @ gmail com
History
2022-05-05: last of 2 revisions
See all versions
Short URL
https://ia.cr/2022/210

CC BY

BibTeX

@misc{cryptoeprint:2022/210,
author = {Jonathan Katz and Cong Zhang and Hong-Sheng Zhou},
title = {An Analysis of the Algebraic Group Model},
howpublished = {Cryptology ePrint Archive, Paper 2022/210},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/210}},
url = {https://eprint.iacr.org/2022/210}
}

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