### Updatable Encryption from Group Actions

##### Abstract

Updatable Encryption (UE) allows to rotate the encryption key in the outsourced storage setting while minimizing the bandwith used. The server can update ciphertexts to the new key using a token provided by the client. UE schemes should provide strong confidentiality guarantees against an adversary that can corrupt keys and tokens. This paper solves three open problems in ciphertext-independent post-quantum UE. First, we propose the first two post-quantum CCA secure UE schemes, solving an open problem left by Jiang at Asiacrypt 2020. Second, our three UE schemes are the first post-quantum schemes that support an unbounded number of updates. Third, the security of our three schemes is based on three different problems which are not lattice problems, whereas the two prior post-quantum UE schemes are both based on LWE. We do so by studying the problem of building UE in the group action framework. We introduce a new notion of Mappable Effective Group Action (MEGA) and show that we can build UE from a MEGA by generalizing the SHINE construction of Boyd et al. at Crypto 2020. We propose two post-quantum instantiations of our UE scheme using some recent group action constructions. Isogeny-based group actions are the most studied post-quantum group actions. Unfortunately, the resulting group actions are not mappable. We show that we can still build UE from isogenies by introducing a new algebraic structure called Effective Triple Orbital Group Action (ETOGA). We prove that UE can be built from an ETOGA and show how to instantiate this abstract structure from isogeny-based group actions.

Available format(s)
Category
Cryptographic protocols
Publication info
Preprint.
Keywords
Updatable Encryption Group Actions Isogenies Post-Quantum Cryptography
Contact author(s)
antonin leroux @ polytechnique org
romeas @ lix polytechnique fr
History
2022-06-09: approved
See all versions
Short URL
https://ia.cr/2022/739

CC BY-NC

BibTeX

@misc{cryptoeprint:2022/739,
author = {Antonin Leroux and Maxime Roméas},
title = {Updatable Encryption from Group Actions},
howpublished = {Cryptology ePrint Archive, Paper 2022/739},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/739}},
url = {https://eprint.iacr.org/2022/739}
}

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