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.
Category / Keywords: foundations / indistinguishability obfuscation, algebraic group model, Schnorr signatures Original Publication (with major differences): IACR-EUROCRYPT-2020 Date: received 23 Jan 2020, last revised 30 Jan 2020 Contact author: thomas agrikola at gmail com,thomas agrikola@kit edu,jkastner@student ethz ch Available format(s): PDF | BibTeX Citation Version: 20200130:193306 (All versions of this report) Short URL: ia.cr/2020/070