We model and analyze the Signal end-to-end messaging protocol within the UC framework. In particular:
- We formulate an ideal functionality that captures end-to-end secure messaging, in a setting with PKI and an untrusted server, against an adversary that has full control over the network and can adaptively and momentarily compromise parties at any time and obtain their entire internal states. In particular our analysis captures the forward secrecy and recovery-of-security properties of Signal and the conditions under which they break.
- We model the main components of the Signal architecture (PKI and long-term keys, the backbone continuous-key-exchange or "asymmetric ratchet," epoch-level symmetric ratchets, authenticated encryption) as individual ideal functionalities that are realized and analyzed separately and then composed using the UC and Global-State UC theorems.
- We show how the ideal functionalities representing these components can be realized using standard cryptographic primitives under minimal hardness assumptions.
Our modeling introduces additional innovations that enable arguing about the security of Signal irrespective of the underlying communication medium, as well as secure composition of dynamically generated modules that share state. These features, together with the basic modularity of the UC framework, will hopefully facilitate the use of both Signal-as-a-whole and its individual components within cryptographic applications.
Two other features of our modeling are the treatment of fully adaptive corruptions, and making minimal use of random oracle abstractions. In particular, we show how to realize continuous key exchange in the plain model, while preserving security against adaptive corruptions.
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EasyUC: Using EasyCrypt to Mechanize Proofs of Universally Composable Security
We present a methodology for using the EasyCrypt proof assistant (originally designed for mechanizing the generation of proofs of game-based security of cryptographic schemes and protocols) to mechanize proofs of security of cryptographic protocols within the universally composable (UC) security framework. This allows, for the first time, the mechanization and formal verification of the entire sequence of steps needed for proving simulation-based security in a modular way:
* Specifying a protocol and the desired ideal functionality.
* Constructing a simulator and demonstrating its validity, via reduction to hard computational problems.
* Invoking the universal composition operation and demonstrating that it indeed preserves security.
We demonstrate our methodology on a simple example: stating and proving the security of secure message communication via a one-time pad, where the key comes from a Diffie-Hellman key-exchange, assuming ideally authenticated communication. We first put together EasyCrypt-verified proofs that: (a) the Diffie-Hellman protocol UC-realizes an ideal key-exchange functionality, assuming hardness of the Decisional Diffie-Hellman problem, and (b) one-time-pad encryption, with a key obtained using ideal key-exchange, UC-realizes an ideal secure-communication functionality. We then mechanically combine the two proofs into an EasyCrypt-verified proof that the composed protocol realizes the same ideal secure-communication functionality.
Although formulating a methodology that is both sound and workable has proven to be a complex task, we are hopeful that it will prove to be the basis for mechanized UC security analyses for significantly more complex protocols.
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- Award ID(s):
- 1801564
- NSF-PAR ID:
- 10095463
- Date Published:
- Journal Name:
- 32nd IEEE Computer Security Foundations Symposium (CSF 2019)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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