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+\begin{thebibliography}{10}
+
+\bibitem{Albrecht_Dowling_Jones}
+Martin~R Albrecht, Benjamin Dowling, and Daniel Jones.
+\newblock Device-oriented group messaging: A formal cryptographic analysis of
+  matrix’ core.
+
+\bibitem{Albrecht_2025}
+Martin~R Albrecht, Benjamin Dowling, and Daniel Jones.
+\newblock Formal analysis of multi-device group messaging in whatsapp.
+
+\bibitem{alwen_doubleratchet}
+Joël Alwen, Sandro Coretti, and Yevgeniy Dodis.
+\newblock {\em The Double Ratchet: Security Notions, Proofs, and Modularization
+  for the Signal Protocol}, volume 11476 of {\em Lecture Notes in Computer
+  Science}, page 129–158.
+\newblock Springer International Publishing, Cham, 2019.
+
+\bibitem{Alwen_Coretti_Jost_Mularczyk_2020}
+Joël Alwen, Sandro Coretti, Daniel Jost, and Marta Mularczyk.
+\newblock {\em Continuous Group Key Agreement with Active Security}, volume
+  12551 of {\em Lecture Notes in Computer Science}, page 261–290.
+\newblock Springer International Publishing, Cham, 2020.
+
+\bibitem{Balbas_SK}
+David Balbás, Daniel Collins, and Phillip Gajland.
+\newblock {\em WhatsUpp with Sender Keys? Analysis, Improvements and Security
+  Proofs}, volume 14442 of {\em Lecture Notes in Computer Science}, page
+  307–341.
+\newblock Springer Nature Singapore, Singapore, 2023.
+
+\bibitem{SoK_CAC}
+Manuel Barbosa, Gilles Barthe, Karthik Bhargavan, Bruno Blanchet, Cas Cremers,
+  Kevin Liao, and Bryan Parno.
+\newblock Sok: Computer-aided cryptography.
+\newblock In {\em 2021 IEEE Symposium on Security and Privacy (SP)}, page
+  777–795, May 2021.
+
+\bibitem{rfc9420}
+Richard Barnes, Benjamin Beurdouche, Raphael Robert, Jon Millican, Emad Omara,
+  and Katriel Cohn-Gordon.
+\newblock {The Messaging Layer Security (MLS) Protocol}.
+\newblock RFC 9420, July 2023.
+
+\bibitem{rfc9180}
+Richard Barnes, Karthikeyan Bhargavan, Benjamin Lipp, and Christopher~A. Wood.
+\newblock {Hybrid Public Key Encryption}.
+\newblock RFC 9180, February 2022.
+
+\bibitem{Basin_Cremers_Dreier_Sasse_2022}
+David Basin, Cas Cremers, Jannik Dreier, and Ralf Sasse.
+\newblock Tamarin: Verification of large-scale, real-world, cryptographic
+  protocols.
+\newblock {\em IEEE Security \& Privacy}, 20(3):24–32, May 2022.
+
+\bibitem{bhargavan_dy}
+Karthikeyan Bhargavan, Abhishek Bichhawat, Quoc~Huy Do, Pedram Hosseyni, Ralf
+  Küsters, Guido Schmitz, and Tim Würtele.
+\newblock Dy*: A modular symbolic verification framework for executable
+  cryptographic protocol code.
+
+\bibitem{DY}
+Karthikeyan Bhargavan, Abhishek Bichhawat, Quoc~Huy Do, Pedram Hosseyni, Ralf
+  Küsters, Guido Schmitz, and Tim Würtele.
+\newblock Dy*: A modular symbolic verification framework for executable
+  cryptographic protocol code.
+
+\bibitem{Bhargavan_PQXDH}
+Karthikeyan Bhargavan, Charlie Jacomme, Franziskus Kiefer, and Rolfe Schmidt.
+\newblock Formal verification of the pqxdh post-quantum key agreement protocol
+  for end-to-end secure messaging.
+
+\bibitem{Blanchet_2012}
+Bruno Blanchet.
+\newblock {\em Security Protocol Verification: Symbolic and Computational
+  Models}, volume 7215 of {\em Lecture Notes in Computer Science}, page 3–29.
+\newblock Springer Berlin Heidelberg, Berlin, Heidelberg, 2012.
+
+\bibitem{Blanchet_2016}
+Bruno Blanchet.
+\newblock Modeling and verifying security protocols with the applied pi
+  calculus and proverif.
+\newblock {\em Foundations and Trends® in Privacy and Security},
+  1(1–2):1–135, 2016.
+
+\bibitem{Blanchet_Jacomme}
+Bruno Blanchet and Charlie Jacomme.
+\newblock Cryptoverif: a computationally-sound security protocol verifier.
+
+\bibitem{ProverifManual}
+Bruno Blanchet, Ben Smyth, Vincent Cheval, and Marc Sylvestre.
+\newblock Proverif 2.05: Automatic cryptographic protocol verifier, user manual
+  and tutorial.
+
+\bibitem{Celi_Hoyland_Stebila_Wiggers_2022}
+Sofía Celi, Jonathan Hoyland, Douglas Stebila, and Thom Wiggers.
+\newblock {\em A Tale of Two Models: Formal Verification of KEMTLS via
+  Tamarin}, volume 13556 of {\em Lecture Notes in Computer Science}, page
+  63–83.
+\newblock Springer Nature Switzerland, Cham, 2022.
+
+\bibitem{Chase_Perrin_Zaverucha_2020}
+Melissa Chase, Trevor Perrin, and Greg Zaverucha.
+\newblock The signal private group system and anonymous credentials supporting
+  efficient verifiable encryption.
+\newblock In {\em Proceedings of the 2020 ACM SIGSAC Conference on Computer and
+  Communications Security}, page 1445–1459, Virtual Event USA, October 2020.
+  ACM.
+
+\bibitem{cremers_signal}
+Katriel Cohn-Gordon, Cas Cremers, Benjamin Dowling, Luke Garratt, and Douglas
+  Stebila.
+\newblock A formal security analysis of the signal messaging protocol.
+
+\bibitem{Collins_Colombo_Huguenin-Dumittan_2025}
+Daniel Collins, Simone Colombo, and Loïs Huguenin-Dumittan.
+\newblock Real-world deniability in messaging.
+\newblock {\em Proceedings on Privacy Enhancing Technologies},
+  2025(1):320–340, January 2025.
+
+\bibitem{auth}
+Whitfield Diffie, Paul~C. Van~Oorschot, and Michael~J. Wiener.
+\newblock Authentication and authenticated key exchanges.
+\newblock {\em Designs, Codes and Cryptography}, 2(2):107–125, June 1992.
+
+\bibitem{Dingledine_Mathewson_Syverson_2004}
+Roger Dingledine, Nick Mathewson, and Paul Syverson.
+\newblock Tor: The second-generation onion router:.
+\newblock January 2004.
+
+\bibitem{Dolev_1983}
+Danny Dolev.
+\newblock On the security of public key protocols.
+\newblock {\em IEEE TRANSACTIONS ON INFORMATION THEORY}, (2), 1983.
+
+\bibitem{Donenfeld_2017}
+Jason~A. Donenfeld.
+\newblock Wireguard: Next generation kernel network tunnel.
+\newblock In {\em Proceedings 2017 Network and Distributed System Security
+  Symposium}, San Diego, CA, 2017. Internet Society.
+
+\bibitem{rfc9369}
+Martin Duke.
+\newblock {QUIC Version 2}.
+\newblock RFC 9369, May 2023.
+
+\bibitem{FiedlerPQXDHdeny}
+Rune Fiedler and Christian Janson.
+\newblock A deniability analysis of signal’s initial handshake pqxdh.
+\newblock {\em Proceedings on Privacy Enhancing Technologies},
+  2024(4):907–928, October 2024.
+
+\bibitem{Gancher_2023}
+Joshua Gancher, Sydney Gibson, Pratap Singh, Samvid Dharanikota, and Bryan
+  Parno.
+\newblock Owl: Compositional verification of security protocols via an
+  information-flow type system.
+\newblock In {\em 2023 IEEE Symposium on Security and Privacy (SP)}, page
+  1130–1147, San Francisco, CA, USA, May 2023. IEEE.
+
+\bibitem{pqwg}
+Andreas Hülsing, Kai-Chun Ning, Peter Schwabe, Fiona~Johanna Weber, and
+  Philip~R. Zimmermann.
+\newblock Post-quantum wireguard.
+\newblock In {\em 2021 IEEE Symposium on Security and Privacy (SP)}, page
+  304–321, San Francisco, CA, USA, May 2021. IEEE.
+
+\bibitem{Itkis_Reyzin_2001}
+Gene Itkis and Leonid Reyzin.
+\newblock {\em Forward-Secure Signatures with Optimal Signing and Verifying},
+  volume 2139 of {\em Lecture Notes in Computer Science}, page 332–354.
+\newblock Springer Berlin Heidelberg, Berlin, Heidelberg, 2001.
+
+\bibitem{Jefferys2020SessionProtocol}
+Kee Jefferys.
+\newblock Session protocol: Technical implementation details.
+\newblock Blog post on getSession.org, December 2020.
+\newblock Accessed: 2025-08-08.
+
+\bibitem{Kobeissi_Bhargavan_Blanchet_2017}
+Nadim Kobeissi, Karthikeyan Bhargavan, and Bruno Blanchet.
+\newblock Automated verification for secure messaging protocols and their
+  implementations: A symbolic and computational approach.
+\newblock In {\em 2017 IEEE European Symposium on Security and Privacy}, page
+  435–450, Paris, April 2017. IEEE.
+
+\bibitem{rfc5869}
+Hugo Krawczyk and Pasi Eronen.
+\newblock {HMAC-based Extract-and-Expand Key Derivation Function (HKDF)}.
+\newblock RFC 5869, May 2010.
+
+\bibitem{Kret_Schmidt_PQXDH}
+Ehren Kret and Rolfe Schmidt.
+\newblock The pqxdh key agreement protocol.
+\newblock 2024.
+
+\bibitem{Lafourcade_Mahmoud_Ruhault_Taleb}
+Pascal Lafourcade, Dhekra Mahmoud, Sylvain Ruhault, and Abdul~Rahman Taleb.
+\newblock A tale of two worlds, a formal story of wireguard hybridization.
+
+\bibitem{Moxie_Sesame}
+Moxie Marlinspike and Trevor Perrin.
+\newblock The sesame algorithm: Session management for asynchronous message
+  encryption.
+\newblock 2016.
+
+\bibitem{Marlinspike_Perrin_X3DH}
+Moxie Marlinspike and Trevor Perrin.
+\newblock The x3dh key agreement protocol.
+\newblock 2016.
+
+\bibitem{matrixorg_olm_repo}
+{matrix-org}.
+\newblock Olm.
+\newblock \url{https://gitlab.matrix.org/matrix-org/olm}, April 2019.
+\newblock GitLab repository implementing Olm and Megolm cryptographic ratchets.
+
+\bibitem{matrixorg_megolm_doc}
+{matrix-org}.
+\newblock docs/megolm.md.
+\newblock
+  \url{https://gitlab.matrix.org/matrix-org/olm/-/blob/master/docs/megolm.md},
+  September 2022.
+\newblock Markdown file in \emph{Olm} repository.
+
+\bibitem{mcmillion2025keytransparencyarchitecture}
+Brendan McMillion.
+\newblock Key transparency architecture.
+\newblock Internet-Draft, IETF, July 2025.
+\newblock draft-ietf-keytrans-architecture-04, Intended status: Informational.
+
+\bibitem{mcMillion2025keytrans}
+Brendan McMillion.
+\newblock {Key Transparency Architecture}.
+\newblock Internet-Draft draft-ietf-keytrans-architecture-04, IETF
+  Internet-Draft, July 2025.
+\newblock Intended status: Informational; Expires 8 January 2026.
+
+\bibitem{MetaMessengerE2EE2023}
+Jon Millican, Reed Riley, and Meta Platforms.
+\newblock Messenger end-to-end encryption overview.
+\newblock Technical White Paper Version 1M, Meta Platforms (Facebook
+  Engineering), December 2023.
+\newblock Published December 6, 2023 — describes core Signal-Protocol-based
+  E2EE implementation for Messenger and Instagram Direct.
+
+\bibitem{Moxie_DoubleRatchet}
+Trevor Perrin and Moxie Marlinspike.
+\newblock The double ratchet algorithm.
+\newblock 2016.
+
+\bibitem{rfc8446}
+Eric Rescorla.
+\newblock {The Transport Layer Security (TLS) Protocol Version 1.3}.
+\newblock RFC 8446, August 2018.
+
+\bibitem{Schwabe_Stebila_Wiggers_2020}
+Peter Schwabe, Douglas Stebila, and Thom Wiggers.
+\newblock Post-quantum tls without handshake signatures.
+\newblock In {\em Proceedings of the 2020 ACM SIGSAC Conference on Computer and
+  Communications Security}, page 1461–1480, Virtual Event USA, October 2020.
+  ACM.
+
+\bibitem{SignalSenderKeysRust}
+{Signal Foundation}.
+\newblock sender\_keys.rs — sender keys implementation (rust).
+\newblock
+  \url{https://github.com/signalapp/libsignal/blob/main/rust/protocol/src/sender\_keys.rs},
+  2025.
+\newblock Reference implementation of the Sender Keys protocol in libsignal’s
+  Rust codebase.
+
+\bibitem{Unger_Goldberg_2018}
+Nik Unger and Ian Goldberg.
+\newblock Improved strongly deniable authenticated key exchanges for secure
+  messaging.
+\newblock {\em Proceedings on Privacy Enhancing Technologies}, 2018(1):21–66,
+  January 2018.
+
+\bibitem{VatandasDeny}
+Nihal Vatandas, Rosario Gennaro, Bertrand Ithurburn, and Hugo Krawczyk.
+\newblock {\em On the Cryptographic Deniability of the Signal Protocol}, volume
+  12147 of {\em Lecture Notes in Computer Science}, page 188–209.
+\newblock Springer International Publishing, Cham, 2020.
+
+\bibitem{Wallez_TreeKEM}
+Theophile Wallez, Jonathan Protzenko, and Karthikeyan Bhargavan.
+\newblock Treekem: A modular machine-checked symbolic security analysis of
+  group key agreement in messaging layer security.
+
+\bibitem{Wallez_TreeSync}
+Théophile Wallez, Benjamin Beurdouche, and Karthikeyan Bhargavan.
+\newblock Treesync: Authenticated group management for messaging layer
+  security.
+
+\bibitem{WhatsAppSecurity2024}
+WhatsApp.
+\newblock Whatsapp encryption overview: Technical white paper.
+\newblock Technical White Paper Version 8, Meta (WhatsApp), August 2024.
+\newblock Updated August 19, 2024.
+
+\bibitem{openvpn}
+James Yonan.
+\newblock {\em OpenVPN: An Open Source VPN}, 2002.
+\newblock Version 2.6.0 and later. Accessed: 2025-08-08.
+
+\end{thebibliography}