Welcome to the resource topic for 2022/1124
Title:
Unbounded Quadratic Functional Encryption and More from Pairings
Authors: Junichi Tomida
Abstract:We propose the first unbounded functional encryption (FE) scheme for quadratic functions and its extension, in which the sizes of messages to be encrypted are not a priori bounded.
Prior to our work, all FE schemes for quadratic functions are bounded, meaning that the message length is fixed at the setup.
In the first scheme, encryption takes \{x_{i}\}_{i \in S_{c}}, key generation takes \{c_{i,j}\}_{i,j \in S_{k}}, and decryption outputs \sum_{i,j \in S_{k}} c_{i,j}x_{i}x_{j} if and only if S_{k} \subseteq S_{c}, where the sizes of S_{c} and S_{k} can be arbitrary.
Our second scheme is the extension of the first scheme to partially-hiding FE that computes an arithmetic branching program on a public input and a quadratic function on a private input.
Concretely, encryption takes a public input \vec{u} in addition to \{x_{i}\}_{i \in S_{c}}, a secret key is associated with arithmetic branching programs \{f_{i,j}\}_{i,j \in S_{k}}, and decryption yields \sum_{i,j \in S_{k}} f_{i,j}(\vec{u})x_{i}x_{j} if and only if S_{k} \subseteq S_{c}.
Both our schemes are based on pairings and secure under the standard MDDH assumption.
ePrint: https://eprint.iacr.org/2022/1124
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