Algebraic Adversaries in the Universal Composability Framework

Abdalla, Michel and Barbosa, Manuel and Katz, Jonathan and Loss, Julian and Xu, Jiayu
(2021) Algebraic Adversaries in the Universal Composability Framework.
In: 27th Annual International Conference on the Theory and Application of Cryptology and Information Security.
Conference: ASIACRYPT International Conference on the Theory and Application of Cryptology and Information Security

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Abstract

he 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.

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