Functional Encryption for Attribute-Weighted Sums from k-Lin

Abstract

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 N i =1 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.

(Inner-Product) Functional Encryption with Updatable Ciphertexts

“…. Then, let c 0 , c 1 consist of c 0 , c 1 in lexicographic order, 13 and the challenger responds with P f,t ← iO(PKey:2…”

“…One such approach that attracted a lot of research are FE schemes for the inner-product functionality (IPFE), i.e., keys are associated with vectors , messages are vectors and decryption reveals . Initially proposed by Abdalla et al [ 2 ], a line of work improved the security guarantees [ 3 , 13 , 15 , 16 , 24 ], extended it to the multi-input [ 8 , 12 ] as well as the decentralized setting [ 4 – 6 , 22 , 46 ]. Although this functionality is very simple, it has already shown to be useful in privacy-preserving machine learning [ 49 ], money-laundering detection [ 31 ], search in encrypted data streams [ 18 ], video data analytics, 2 or data marketplaces [ 43 ].…”