Efficient Function-Hiding Functional Encryption - From Inner-Products to Orthogonality.

We construct functional encryption (FE) schemes for the orthogonality (OFE) relation where each ciphertext encrypts some vector (varvec{mathsf {x}}) and each decryption key, associated to some vector (varvec{mathsf {y}}), allows to determine if (varvec{mathsf {x}}) is orthogonal to (varvec{mathsf {y}}) or not. Motivated by compelling applications, we aim at schemes which are function hidding, i.e. (varvec{mathsf {y}}) is not leaked.