Functional Encryption for Attribute-Weighted Sums from k-Lin

We present functional encryption schemes for attribute-weighted sums, where encryption takes as input $N$ attribute-value pairs $(x_i,z_i)$ where $x_i$ is public and $z_i$ is private; secret keys are associated with arithmetic branching programs $f$, and decryption returns the weighted sum $\sum_{i=1}^N f(x_i) z_i$ while leaking no additional information about the $z_i$'s. Our main construction achieves

(1) compact public parameters and key sizes that are independent of $N$ and the secret key can decrypt a ciphertext for any a-prior unbounded $N$;

(2) short ciphertexts that grow with $N$ and the size of $z_i$ but not $x_i$;

(3) simulation-based security against unbounded collusions;

(4) relies on the standard $k$-linear assumption in prime-order bilinear groups.