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Algebraic Adversaries in the Universal Composability Framework

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conference contribution
posted on 2023-11-29, 18:18 authored by Michel Abdalla, Manuel Barbosa, Jonathan Katz, Julian LossJulian Loss, Jiayu Xu
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.

History

Preferred Citation

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

Primary Research Area

  • Reliable Security Guarantees

Name of Conference

International Conference on the Theory and Application of Cryptology and Information Security (ASIACRYPT)

Legacy Posted Date

2022-01-05

Open Access Type

  • Unknown

BibTeX

@inproceedings{cispa_all_3528, title = "Algebraic Adversaries in the Universal Composability Framework", author = "Abdalla, Michel and Barbosa, Manuel and Katz, Jonathan and Loss, Julian and Xu, Jiayu", booktitle="{International Conference on the Theory and Application of Cryptology and Information Security (ASIACRYPT)}", year="2021", }

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