An Analysis of the Algebraic Group Model

• Published in: Advances in Cryptology - ASIACRYPT 2022 Vol. 13794; pp. 310 - 322
• Main Authors: Zhang, Cong, Zhou, Hong-Sheng, Katz, Jonathan
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer 2023; Springer Nature Switzerland
• Series: Lecture Notes in Computer Science
• ISBN: 3031229711; 9783031229718
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-031-22972-5_11

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.