Mechanized Proofs of Adversarial Complexity and Application to Universal Composability
Authors: 
Manuel Barbosa, Gilles Barthe, Benjamin Grégoire, Adrien Koutsos, Pierre-Yves StrubAuthors Info & Claims
Article No.: 41, Pages 1 - 34
Abstract
In this work, we enhance the EasyCrypt proof assistant to reason about the computational complexity of adversaries. The key technical tool is a Hoare logic for reasoning about computational complexity (execution time and oracle calls) of adversarial computations. Our Hoare logic is built on top of the module system used by EasyCrypt for modeling adversaries. We prove that our logic is sound w.r.t. the semantics of EasyCrypt programs—we also provide full semantics for the EasyCrypt module system, which was lacking previously.
We showcase (for the first time in EasyCrypt and in other computer-aided cryptographic tools) how our approach can express precise relationships between the probability of adversarial success and their execution time. In particular, we can quantify existentially over adversaries in a complexity class and express general composition statements in simulation-based frameworks. Moreover, such statements can be composed to derive standard concrete security bounds for cryptographic constructions whose security is proved in a modular way. As a main benefit of our approach, we revisit security proofs of some well-known cryptographic constructions and present a new formalization of universal composability.
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Index Terms
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Publication History
Published: 19 July 2023
Online AM: 31 March 2023
Accepted: 13 March 2023
Received: 22 August 2022
Published in TOPS Volume 26, Issue 3
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- French National Research Agency (ANR)
- National Funds through the FCT (Fundação para a Ciência e a Tecnologia)
- France 2030 program managed by the French National Research Agency
- Office of Naval Research (ONR)
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