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arXiv:2301.07045

Analysis and Improvements of the Sender Keys Protocol for Group Messaging

Balbás, David, Collins, Daniel, Gajland, Phillip

Published Jan 17, 2023• 2 citations
arXivHTMLPDF

Abstract

Messaging between two parties and in the group setting has enjoyed widespread attention both in practice, and, more recently, from the cryptographic community. One of the main challenges in the area is constructing secure (end-to-end encrypted) and efficient messaging protocols for group conversations. The popular messaging applications WhatsApp and Signal utilise a protocol in which, instead of sharing a single group key, members have individual \textit{sender keys}, which are shared with all other group members. The Sender Keys protocol is claimed to offer forward security guarantees. However, despite its broad adoption in practice, it has never been studied formally in the cryptographic literature. In this paper we present the first analysis of the Sender Keys protocol along with some prospective improvements. To this end, we introduce a new cryptographic primitive, develop a game-based security model, present a security analysis in the passive and active settings, and propose several improvements to the protocol.

DOI
10.48550/arxiv.2301.07045

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Messaging between two parties and in the group setting has enjoyed widespread attention both in practice, and, more recently, from the cryptographic community. One of the main challenges in the area is constructing secure (end-to-end encrypted) and efficient messaging protocols for group conversations. The popular messaging applications WhatsApp and Signal utilise a protocol in which, instead of sharing a single group key, members have individual \textit{sender keys}, which are shared with all other group members. The Sender Keys protocol is claimed to offer forward security guarantees. However, despite its broad adoption in practice, it has never been studied formally in the cryptographic literature. In this paper we present the first analysis of the Sender Keys protocol along with some prospective improvements. To this end, we introduce a new cryptographic primitive, develop a game-based security model, present a security analysis in the passive and active settings, and propose several improvements to the protocol.
In 2004, Hwang et al. proposed a group key exchange protocol for sharing a secure key in a group. Their protocol is an extension from the two party key exchange protocol to the group one. Recently, Jung-San Lee et al. noted that Hwang et al. group key exchange protocol has two security weaknesses. First, the forward secrecy is not confirmed in case that a new member joins the group and second, if a group member leaves the group, the backward secrecy is compromised. They proposed an improvement over this key exchange protocol in order to provide both forward and backward secrecy among group members. In this paper, we propose another improvement over Lee et al. key exchange, and we show that our key exchange protocol not only preservers both forward and backward secrecy, but also it is more efficient than their protocol when a member leaves the group. Finally, we give a formal analysis for the correctness of the proposed protocol via Scyther model checking tool.
Secure group messaging protocols, providing end-to-end encryption for group communication, need to handle mobile devices frequently being offline, group members being added or removed, and the possibility of device compromises during long-lived chat sessions. Existing work targets a centralized network model in which all messages are routed through a single server, which is trusted to provide a consistent total order on updates to the group state. In this paper we adapt secure group messaging for decentralized networks that have no central authority. Servers may still optionally be used, but they are trusted less. We define decentralized continuous group key agreement (DCGKA), a new cryptographic primitive encompassing the core of a decentralized secure group messaging protocol; we give a practical construction of a DCGKA protocol and prove its security; and we describe how to construct a full messaging protocol from DCGKA. In the face of device compromise our protocol achieves forward secrecy and post-compromise security. We evaluate the performance of a prototype implementation, and demonstrate that our protocol has practical efficiency.
Signal is a new security protocol and accompanying app that provides end-to-end encryption for instant messaging. The core protocol has recently been adopted by WhatsApp, Facebook Messenger, and Google Allo among many others, the first two of these have at least 1 billion active users. Signal includes several uncommon security properties (such as "future secrecy" or "post-compromise security"), enabled by a novel technique called ratcheting in which session keys are updated with every message sent. Despite its importance and novelty, there has been little to no academic analysis of the Signal protocol. We conduct the first security analysis of Signal's key agreement and double ratchet as a multi-stage key exchange protocol. We extract from the implementation a formal description of the abstract protocol, and define a security model which can capture the "ratcheting" key update structure. We then prove the security of Signal's core in our model, demonstrating several standard security properties. We have found no major flaws in the design, and hope that our presentation and results can serve as a starting point for other analyses of this widely adopted protocol.
Focusing on its cryptographic core, we provide the first formal description of the Matrix secure group messaging protocol. Observing that no existing secure messaging model in the literature captures the relationships (and shared state) between users, their devices and the groups they are a part of, we introduce the Device-Oriented Group Messaging model to capture these key characteristics of the Matrix protocol. Utilising our new formalism, we determine that Matrix achieves the basic security notions of confidentiality and authentication, provided it introduces authenticated group membership. On the other hand, while the state sharing functionality in Matrix conflicts with advanced security notions in the literature – forward and post-compromise security – it enables features such as history sharing and account recovery, provoking broader questions about how such security notions should be conceptualised.
A recent primitive known as asymmetric group key agreement allows a group of users to negotiate a common encryption key which is accessible to any entities while each user holds her respective secret decryption key. This concept not only enables confidential communications among group users but also permits any outsider to send encrypted messages to the group. The existing instantiation is only secure against passive adversaries. In this paper, we first propose an authenticated asymmetric group key agreement protocol which captures the practical security properties against active attacks. Based on our protocol, we then propose a broadcast encryption system without relying on a trusted dealer to distribute the secret keys to the users. Our system has also short ciphertexts. Furthermore, the proposal is equipped with the perfect forward security property.
In the past few years secure messaging has become mainstream, with over a billion active users of end-to-end encryption protocols such as Signal. The Signal Protocol provides a strong property called post-compromise security to its users. However, it turns out that many of its implementations provide, without notification, a weaker property for group messaging: an adversary who compromises a single group member can read and inject messages indefinitely. We show for the first time that post-compromise security can be achieved in realistic, asynchronous group messaging systems. We present a design called Asynchronous Ratcheting Trees (ART), which uses tree-based Diffie-Hellman key exchange to allow a group of users to derive a shared symmetric key even if no two are ever online at the same time. ART scales to groups containing thousands of members, while still providing provable security guarantees. It has seen significant interest from industry, and forms the basis for two draft IETF RFCs and a chartered working group. Our results show that strong security guarantees for group messaging are practically achievable in a modern setting.