Paper 2022/210

An Analysis of the Algebraic Group Model

Jonathan Katz, University of Maryland, College Park
Cong Zhang, Zhejiang University
Hong-Sheng Zhou, Virginia Commonwealth University

The algebraic group model (AGM), formalized by Fuchsbauer, Kiltz, and Loss, has recently received significant attention. One of the appealing properties of the AGM is that it is viewed as being (strictly) weaker than the generic group model (GGM), in the sense that hardness results for algebraic algorithms imply hardness results for generic algorithms, and generic reductions in the AGM (namely, between the algebraic formulations of two problems) imply generic reductions in the GGM. We highlight that as the GGM and AGM are currently formalized, this is not true: hardness in the AGM may not imply hardness in the GGM, and a generic reduction in the AGM may not imply a similar reduction in the GGM.

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Published by the IACR in ASIACRYPT 2022
idealized models generic group model
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jkatz @ cs umd edu
congresearch @ gmail com
hszhou @ vcu edu
2022-10-01: last of 4 revisions
2022-02-22: received
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      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{}},
      url = {}
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