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Conference Papers Year : 2021

Algebraic Adversaries in the Universal Composability Framework


The algebraic-group model (AGM), which lies between the generic group model and the standard model of computation, provides a means by which to analyze the security of cryptosystems against so-called algebraic adversaries. We formalize the AGM within the framework of universal com-posability, providing formal definitions for this setting and proving an appropriate composition theorem. This extends the applicability of the AGM to more-complex protocols, and lays the foundations for analyzing algebraic adversaries in a composable fashion. Our results also clarify the meaning of com-posing proofs in the AGM with other proofs and they highlight a natural form of independence between idealized groups that seems inherent to the AGM and has not been made formal before—these insights also apply to the composition of game-based proofs in the AGM. We show the utility of our model by proving several important protocols universally composable for algebraic adversaries, specifically:(1) the Chou-Orlandi protocol for oblivious transfer, and (2) the SPAKE2 and CPace protocols for password-based authenticated key exchange.

Dates and versions

hal-03517558 , version 1 (07-01-2022)



Michel Abdalla, Manuel Barbosa, Jonathan Katz, Julian Loss, Jiayu Xu. Algebraic Adversaries in the Universal Composability Framework. ASIACRYPT 2021 - 27th International Conference on the Theory and Application of Cryptology and Information Security, Dec 2021, Singapour, Singapore. pp.311-341, ⟨10.1007/978-3-030-92078-4_11⟩. ⟨hal-03517558⟩
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