Algebraic Adversaries in the Universal Composability Framework

Michel Abdalla (1, 2, 3, 4, 5) , Manuel Barbosa (6, 7) , Jonathan Katz (8) , Julian Loss (9) , Jiayu Xu (10)

1 LIENS - Laboratoire d'informatique de l'école normale supérieure
2 PSL - Université Paris sciences et lettres
3 ENS-PSL - École normale supérieure - Paris
4 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
5 DFINITY Foundation [Zurich]
6 FCUP - Faculdade de Ciências da Universidade do Porto
7 INESC TEC - Institute for Systems and Computer Engineering, Technology and Science [Porto]
8 University of Maryland [Baltimore]
9 CISPA - Helmholtz Center for Information Security [Saarbrücken]
10 Algorand Foundation

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 composability, 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 composing 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.

Domaines: Cryptographie et sécurité [cs.CR]

Michel Abdalla, Manuel Barbosa, Jonathan Katz, Julian Loss, Jiayu Xu. Algebraic Adversaries in the Universal Composability Framework. [Research Report] IACR Cryptology ePrint Archive. 2021. ⟨hal-03442093⟩