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2024 | OriginalPaper | Buchkapitel

Registered Functional Encryptions from Pairings

verfasst von : Ziqi Zhu, Jiangtao Li, Kai Zhang, Junqing Gong, Haifeng Qian

Erschienen in: Advances in Cryptology – EUROCRYPT 2024

Verlag: Springer Nature Switzerland

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Abstract

This work initiates the study of concrete registered functional encryption (Reg-FE) beyond “all-or-nothing” functionalities:

We build the first Reg-FE for linear function or inner-product evaluation (Reg-IPFE) from pairings. The scheme achieves adaptive IND-security under k-Lin assumption in the prime-order bilinear group. A minor modification yields the first Registered Inner-Product Encryption (Reg-IPE) scheme from k-Lin assumption. Prior work achieves the same security in the generic group model.
We build the first Reg-FE for quadratic function (Reg-QFE) from pairing. The scheme achieves very selective simulation-based security (SIM-security) under bilateral k-Lin assumption in the prime-order bilinear group. Here, “very selective” means that the adversary claims challenge messages, all quadratic functions to be registered and all corrupted users at the beginning.

Besides focusing on the compactness of the master public key and helper keys, we also aim for compact ciphertexts in Reg-FE. Let L be the number of slots and n be the input size. Our first Reg-IPFE has weakly compact ciphertexts of size \(O(n\cdot \log L)\) while our second Reg-QFE has compact ciphertexts of size \(O(n+\log L)\). Technically, for our first Reg-IPFE, we employ nested dual-system method within the context of Reg-IPFE; for our second Reg-QFE, we follow Wee’s “IPFE-to-QFE” transformation [TCC’ 20] but devise a set of new techniques that make our pairing-based Reg-IPFE compatible. Along the way, we introduce a new notion named Pre-Constrained Registered IPFE which generalizes slotted Reg-IPFE by constraining the form of functions that can be registered.

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Vorheriges Kapitel Circuit Bootstrapping: Faster and Smaller

Nächstes Kapitel Accelerating BGV Bootstrapping for Large p Using Null Polynomials over

Formally, the adversary is given \( \textsf {crs}\) that allows it to derive \( \textsf{mpk}, \textsf {hsk}_1,\ldots , \textsf {hsk}_L\) on its own; our conceptual definition gives a simple mind model analogous to FE.

Here we hardcode master public key and master secret key inside \(\textsf{i}\textsf{Enc}\) and \(\textsf{i}\textsf{Key}\), respectively, for notation simplicity.

The \((k,\ell ,d)\text {-}\textsc {MDDH}\) assumption holds unconditionally when \(\ell > k\).

Note that we use two difference indices i and j for \( \textsf {pk}_i\) and \( \textsf {hsk}_j\), respectively; both of them range from 1 to L.

Note that we employ i as the index for \(\textbf{W}_q\)’s and \(\textbf{M}_q\)’s while j is the index for \(\textbf{r}_q\)’s; both of them range from 1 to \(L_q\). One exception is the terms with \(\textbf{W}_q\), which is conceptually \(\textbf{W}_{q,i}(\textbf{M}_{q,i}\otimes \textbf{B}_q\textbf{r}_{q,j}^{\!\scriptscriptstyle {\top }})\) with \(i=j\). Note that we do not use \(\textsf{td}_{q,1},\ldots ,\textsf{td}_{q,L_q}\) and \(\textsf{i} \textsf {sk}\) in the actual scheme.

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Titel: Registered Functional Encryptions from Pairings
verfasst von: Ziqi Zhu
Jiangtao Li
Kai Zhang
Junqing Gong
Haifeng Qian
Verlag: Springer Nature Switzerland
Buch: Advances in Cryptology – EUROCRYPT 2024
Print ISBN: 978-3-031-58722-1

Electronic ISBN: 978-3-031-58723-8

Copyright-Jahr: 2024
DOI: https://doi.org/10.1007/978-3-031-58723-8_13

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