International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: On Instantiating the Algebraic Group Model from Falsifiable Assumptions

Thomas Agrikola , Karlsruhe Institute of Technology, Karlsruhe, Germany
Dennis Hofheinz , ETH Zurich, Zurich, Switzerland
Julia Kastner , ETH Zurich, Zurich, Switzerland
DOI: 10.1007/978-3-030-45724-2_4 (login may be required)
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Conference: EUROCRYPT 2020
Abstract: We provide a standard-model implementation (of a relaxation) of the algebraic group model (AGM, [Fuchsbauer, Kiltz, Loss, CRYPTO 2018]). Specifically, we show that every algorithm that uses our group is algebraic, and hence "must know" a representation of its output group elements in terms of its input group elements. Here, "must know" means that a suitable extractor can extract such a representation efficiently. We stress that our implementation relies only on falsifiable assumptions in the standard model, and in particular does not use any knowledge assumptions. As a consequence, our group allows to transport a number of results obtained in the AGM into the standard model, under falsifiable assumptions. For instance, we show that in our group, several Diffie-Hellman-like assumptions (including computational Diffie-Hellman) are equivalent to the discrete logarithm assumption. Furthermore, we show that our group allows to prove the Schnorr signature scheme tightly secure in the random oracle model. Our construction relies on indistinguishability obfuscation, and hence should not be considered as a practical group itself. However, our results show that the AGM is a realistic computational model (since it can be instantiated in the standard model), and that results obtained in the AGM are also possible with standard-model groups.
Video from EUROCRYPT 2020
  title={On Instantiating the Algebraic Group Model from Falsifiable Assumptions},
  booktitle={39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10–14, 2020, Proceedings},
  series={Lecture Notes in Computer Science},
  keywords={indistinguishability obfuscation;algebraic group model;Schnorr signatures},
  author={Thomas Agrikola and Dennis Hofheinz and Julia Kastner},