Welcome to the resource topic for
**2022/210**

**Title:**

An Analysis of the Algebraic Group Model

**Authors:**
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. This work analyzes the definition of algebraic algorithms, the notion of generic reduction in AGM, and the relationship between the AGM and Shoup’s GGM (Eurocrypt 1997). The following lists our contributions: 1. the formal definition of algebraic algorithms does \textit{not} capture the intuition of the algebraic algorithms; 2. following the definition of generic algorithms in Shoup’s GGM, the notion of generic reduction in the AGM is not well-defined; 3. two strengthened versions of generic algorithms to make sure the notion of generic reduction in the AGM is well-defined, two strengthened versions of generic algorithms are introduced; 4. hardness of security games in Shoup’s GGM cannot be transferred via a generic reduction in the AGM; 5. the AGM and Shoup’s GGM are incomparable.

**ePrint:**
https://eprint.iacr.org/2022/210

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