(2026-04) Round-Optimal Privacy Preserving Authenticated Key Exchange Even for Incomplete Sessions
2026-04-15
Several modern applications, such as Signal or WireGuard, use efficient Noise-like implicit authentication key exchanges that require only a small number of exponentiations and two interactions. These protocols have been proven to be secure under the 'strong Diffie–Hellman' (SDH) assumption in the random oracle model (ROM). At ESORICS 2021, Ramacher, Slamanig and Weninger presented an extension to the implicit authenticated key exchange security model, which enables strong privacy properties to be captured in addition to key-secrecy, including man-in-the-middle privacy (ensuring privacy even if a session is interrupted) and forward privacy. They also proposed a protocol to instantiate their model. In this paper, we present an efficient Noise-like protocol that achieve privacy in this model. Our protocol is as efficient as Noise-like protocols that do not guarantee privacy in terms of exponentiations. Moreover, our protocol requires three interactions, which is optimal for this privacy model. It is also more efficient than the ESORICS 2021 protocol in terms of both exponentiations and interactions. Finally, we propose another round-optimal protocol, slightly less efficient in terms of exponentiations, but secure under the CDH assumption in the ROM.