Paper 2026/884

Formalizing and Strengthening the Security Proof of NTOR

Kristian Gjøsteen, Norwegian University of Science and Technology

Cameron Low, University of Bristol

Charlotte Mylog, Norwegian University of Science and Technology

Abstract

We present a machine-checked security proof for the NTOR key exchange protocol, which is used to establish connections in the Tor onion routing system. It was previously studied by Goldberg et al. (DCC 2013), but within a slightly non-standard model that did not explicitly capture forward secrecy. Our proof is fully formalized in EasyCrypt, adding to the still small set of cryptographic protocols verified in the computational model. A key contribution is a systematic treatment of halting reductions involving failure events expressed as global properties of the execution. In the course of this work, we also contributed improvements to the EasyCrypt framework itself. We prove NTOR secure in a new model of unilaterally authenticated key exchange that captures forward secrecy, and is intentionally close to established bilaterally AKE models (such as eCK). By examining more carefully how identities and public keys are used in key exchange proto- cols, we obtain simpler formal arguments and introduce several variants of our UAKE security model, connected by general reductions that, in the case of NTOR, are also realized in EasyCrypt. This allows us to carry out the main proof in a simpler setting and then derive the desired security guarantee for NTOR via these reductions.

Note: Adding affiliations and minor changes to the presentation.

@misc{cryptoeprint:2026/884,
      author = {François Dupressoir and Kristian Gjøsteen and Cameron Low and Charlotte Mylog},
      title = {Formalizing and Strengthening the Security Proof of {NTOR}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/884},
      year = {2026},
      url = {https://eprint.iacr.org/2026/884}
}