Welcome to the resource topic for 2020/070
Title:
On Instantiating the Algebraic Group Model from Falsifiable Assumptions
Authors: Thomas Agrikola, Dennis Hofheinz, Julia Kastner
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.
ePrint: https://eprint.iacr.org/2020/070
Talk: https://www.youtube.com/watch?v=gXNvO0nhBzE
Slides: https://iacr.org/submit/files/slides/2020/eurocrypt/ec2020/281/slides.pdf
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .