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The algebraic group model (AGM), formalized by Fuchsbauer, Kiltz, and Loss (Crypto 2018), has recently garnered significant attention. Notably, Katz, Zhang, and Zhou (Asiacrypt 2022) challenged a widely held belief: that hardness results proven in the AGM imply corresponding results in the generic group model (GGM). They showed that this implication fails under Shoup’s GGM framework. In response, Jaeger and Mohan (Crypto 2024) proposed an alternative interpretation based on Maurer’s GGM and proved that, under this interpretation, the implication indeed holds. Many cryptographic applications analyzed in the AGM also rely on the random oracle model (ROM), which is largely absent from Jaeger and Mohan’s framework. Because Maurer’s GGM and the ROM are inherently incomparable, Jaeger and Mohan’s framework may not capture AGM+ROM proofs. To bridge this gap and faithfully translate AGM+ROM proofs into the GGM setting, we make the following contributions:

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Hashing in Generic Groups: Completing the AGM-to-GGM Transfer

  • 会议论文

  • 发表日期：

    2026年

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  • Taiyu Wang,
  • Cong Zhang,
  • Hong-Sheng Zhou,
  • Xin Wang,
  • Keyu Ji,
  • Zhihong Jia,
  • Li Lin,
  • Changzheng Wei,
  • Ying Yan,
  • Kui Ren,
  • Chun Chen

摘要

The algebraic group model (AGM), formalized by Fuchsbauer, Kiltz, and Loss (Crypto 2018), has recently garnered significant attention. Notably, Katz, Zhang, and Zhou (Asiacrypt 2022) challenged a widely held belief: that hardness results proven in the AGM imply corresponding results in the generic group model (GGM). They showed that this implication fails under Shoup’s GGM framework. In response, Jaeger and Mohan (Crypto 2024) proposed an alternative interpretation based on Maurer’s GGM and proved that, under this interpretation, the implication indeed holds. Many cryptographic applications analyzed in the AGM also rely on the random oracle model (ROM), which is largely absent from Jaeger and Mohan’s framework. Because Maurer’s GGM and the ROM are inherently incomparable, Jaeger and Mohan’s framework may not capture AGM+ROM proofs. To bridge this gap and faithfully translate AGM+ROM proofs into the GGM setting, we make the following contributions: