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-priori 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.