International Association
for Cryptologic Research

Recently, Abdalla, Gong and Wee (Crypto 2020) provided the first functional encryption scheme for attribute-weighted sums (AWS), where encryption takes as input $N$ (unbounded) attribute-value pairs $\{\vec{x}_i, \vec{z}_i\}_{I \in [N]}$ where $\vec{x}_i$ is public and $\vec{z}_i$ is private, the secret key is associated with an arithmetic branching programs $f$, and decryption returns the weighted sum ${\sum}_{{i \in [N]}} f(\vec{x}_i)^\top \vec{z}_i$, leaking no additional information about the $\vec{z}_i$'s. We extend FE for AWS to the significantly more challenging multi-party setting and provide the first construction for {\it attribute-based} multi-input FE (MIFE) supporting AWS. For $i \in [n]$, encryptor $i$ can choose an attribute $\vec{y}_i$ together with AWS input $\{\vec{x}_{i,j}, \vec{z}_{i,j}\}$ where $j \in [N_i]$ and $N_i$ is unbounded, the key generator can choose an access control policy $g_i$ along with its AWS function $h_i$ for each $i \in [n]$, and the decryptor can compute

$$\sum_{i \in [n]}\sum_{j \in [N_{i}]}h_{i}(\vec{x}_{i,j})^{\top}\vec{z}_{i,j} \text{ iff } g_{i}(\vec{y}_{i}) =0 \text{ for all } i \in [n]$$ Previously, the only known attribute based MIFE was for the inner product functionality (Abdalla et al.~Asiacrypt 2020), where additionally, $\vec{y}_i$ had to be fixed during setup and must remain the same for all ciphertexts in a given slot. Our attribute based MIFE implies the notion of multi-input {\it attribute based encryption} (\miabe) recently studied by Agrawal, Yadav and Yamada (Crypto 2022) and Francati, Friolo, Malavolta and Venturi (Eurocrypt 2023), for a conjunction of predicates represented as arithmetic branching programs (ABP). Along the way, we also provide the first constructions of multi-client FE (MCFE) and dynamic decentralized FE (DDFE) for the AWS functionality. Previously, the best known MCFE and DDFE schemes were for inner products (Chotard et al.~ePrint 2018, Abdalla, Benhamouda and Gay, Asiacrypt 2019, and Chotard et al.~Crypto 2020). Our constructions are based on pairings and proven selectively secure under the matrix DDH assumption.