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2021 | OriginalPaper | Buchkapitel

Non-interactive CCA2-Secure Threshold Cryptosystems: Achieving Adaptive Security in the Standard Model Without Pairings

verfasst von : Julien Devevey, Benoît Libert, Khoa Nguyen, Thomas Peters, Moti Yung

Erschienen in: Public-Key Cryptography – PKC 2021

Verlag: Springer International Publishing

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Abstract

We consider threshold public-key encryption, where the decryption servers distributively hold the private key shares, and we need a threshold of these servers to decrypt the message (while the system remains secure when less than the threshold is corrupt). We investigate the notion of chosen-ciphertext secure threshold systems which has been historically hard to achieve. We further require the systems to be, both, adaptively secure (i.e., secure against a strong adversary making corruption decisions dynamically during the protocol), and non-interactive (i.e., where decryption servers do not interact amongst themselves but rather efficiently contribute, each, a single message). To date, only pairing-based implementations were known to achieve security in the standard security model without relaxation (i.e., without assuming the random oracle idealization) under the above stringent requirements. Here, we investigate how to achieve the above using other assumptions (in order to understand what other algebraic building blocks and mathematical assumptions are needed to extend the domain of encryption methods achieving the above). Specifically, we show realizations under the Decision Composite Residuosity (\(\mathsf {DCR}\)) and Learning-With-Errors (\(\mathsf {LWE}_{}\)) assumptions.

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Vorheriges Kapitel Subversion-Resilient Public Key Encryption with Practical Watchdogs

Nächstes Kapitel Updatable Signatures and Message Authentication Codes

An alternative approach, suggested in [5, 73], requires each participant to store back-up shares of other participant’s shares in such a way that the missing contributions of faulty servers can be reconstructed. However, it still requires additional interaction.

When \(t,\ell =O(\log \lambda )\), statically secure schemes can be proven adaptively secure by guessing the set of corrupted servers upfront.

Faust et al. [43] showed that Fiat-Shamir provides simulation-soundness “for free” in the ROM. However, their proof crucially relies on the random oracle modeling of hash functions and it is not known to immediately carry over to the standard model.

Note that a threshold-t function can be obtained from the majority function by fixing the desired number of input bits, so that we need a majority function of size \(\le 2\ell \) to construct a threshold function \(T_{t,\ell }\).

It helps defining robustness. For non-robust TPKE, \(\phi \) is the identity function.

While the rate can be optimized via hybrid encryption, this would ruin the voting-friendly property of the scheme [12]. Moreover, the KEM/DEM framework does not immediately work in the threshold setting (see, e.g., [3]).

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Titel: Non-interactive CCA2-Secure Threshold Cryptosystems: Achieving Adaptive Security in the Standard Model Without Pairings
verfasst von: Julien Devevey
Benoît Libert
Khoa Nguyen
Thomas Peters
Moti Yung
Verlag: Springer International Publishing
Buch: Public-Key Cryptography – PKC 2021
Print ISBN: 978-3-030-75244-6

Electronic ISBN: 978-3-030-75245-3

Copyright-Jahr: 2021
DOI: https://doi.org/10.1007/978-3-030-75245-3_24

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