Abstract
The Hybrid Public Key Encryption (HPKE) scheme is an emerging standard currently under consideration by the Crypto Forum Research Group (CFRG) of the IETF as a candidate for formal approval. Of the four modes of HPKE, we analyse the authenticated mode \(\mathsf {HPKE}_\mathsf {Auth}\) in its single-shot encryption form as it contains what is, arguably, the most novel part of HPKE.
\(\mathsf {HPKE}_\mathsf {Auth}\)’s intended application domain is captured by a new primitive which we call Authenticated Public Key Encryption (APKE). We provide syntax and security definitions for APKE schemes, as well as for the related Authenticated Key Encapsulation Mechanisms (AKEMs). We prove security of the AKEM scheme \(\mathsf {DH}\hbox {-}\mathsf {AKEM}\) underlying \(\mathsf {HPKE}_\mathsf {Auth}\) based on the Gap Diffie-Hellman assumption and provide general AKEM/DEM composition theorems with which to argue about \(\mathsf {HPKE}_\mathsf {Auth}\)’s security. To this end, we also formally analyse \(\mathsf {HPKE}_\mathsf {Auth}\)’s key schedule and key derivation functions. To increase confidence in our results we use the automatic theorem proving tool CryptoVerif. All our bounds are quantitative and we discuss their practical implications for \(\mathsf {HPKE}_\mathsf {Auth}\).
As an independent contribution we propose the new framework of nominal groups that allows us to capture abstract syntactical and security properties of practical elliptic curves, including the Curve25519 and Curve448 based groups (which do not constitute cyclic groups).
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Notes
- 1.
The ESNI RFC calls for a client initiating a TLS connection to send an HPKE ciphertext to the server. Although not as common, TLS can also be used in settings with bi-directional authentication. In particular, clients can use certificates binding their identities to their public key to authenticate themselves to the server. Unfortunately, it is unclear how the server would know, a priori, which public key to use for the client when attempting to decrypt the HPKE ciphertext.
- 2.
The only exception we are aware of are the security notions used to analyse 2 bilinear-pairing-based schemes in Sections 5.5 and 5.6 of [18].
- 3.
The exact probability bound is indicated in Lemma 8 of that paper’s full version.
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Acknowledgements
The authors would like to thank the HPKE RFC co-authors Richard Barnes, Karthikeyan Bhargavan, and Christopher Wood for fruitful discussions during the preparation of this paper.
Bruno Blanchet was supported by ANR TECAP (decision number ANR-17-CE39-0004-03). Eduard Hauck was supported by the DFG SPP 1736 Big Data. Eike Kiltz was supported by the BMBF iBlockchain project, the EU H2020 PROMETHEUS project 780701, the DFG SPP 1736 Big Data, and the DFG Cluster of Excellence 2092 CASA. Benjamin Lipp was supported by ERC CIRCUS (grant agreement n\(^\circ \) 683032) and ANR TECAP (decision number ANR-17-CE39-0004-03). Doreen Riepel was supported by the Cluster of Excellence 2092 CASA.
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Alwen, J., Blanchet, B., Hauck, E., Kiltz, E., Lipp, B., Riepel, D. (2021). Analysing the HPKE Standard. In: Canteaut, A., Standaert, FX. (eds) Advances in Cryptology – EUROCRYPT 2021. EUROCRYPT 2021. Lecture Notes in Computer Science(), vol 12696. Springer, Cham. https://doi.org/10.1007/978-3-030-77870-5_4
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