Summary: In a functional encryption scheme, secret keys are associated with functions and ciphertexts are associated with messages. Given a secret key for a function \(f\), and a ciphertext for a message \(x\), a decryptor learns \(f(x)\) and nothing else about \(x\). Inner product encryption is a special case of functional encryption where both secret keys and ciphertext are associated with vectors. The combination of a secret key for a vector \(\mathfrak{x}\) and a ciphertext for a vector \(\mathfrak{y}\) reveal \(\langle{\mathfrak{x}},\mathfrak{y}\rangle\) and nothing more about \(\mathfrak{y}\). An inner product encryption scheme is function-hiding if the keys and ciphertexts reveal no additional information about both \(\mathfrak{x}\) and \(\mathfrak{y}\) beyond their inner product.
In the last few years, there has been a flurry of works on the construction of function-hiding inner product encryption, starting with the work of A. Bishop et al. [Lect. Notes Comput. Sci. 9452, 470–491 (2015; Zbl 1396.94061)] to the more recent work of J. Tomida et al. [ibid. 9866, 408–425 (2016; Zbl 1397.68064)]. In this work, we focus on the practical applications of this primitive. First, we show that the parameter sizes and the run-time complexity of the state-of-the-art construction can be further reduced by another factor of 2, though we compromise by proving security in the generic group model. We then show that function privacy enables a number of applications in biometric authentication, nearest-neighbor search on encrypted data, and single-key two-input functional encryption for functions over small message spaces. Finally, we evaluate the practicality of our encryption scheme by implementing our function-hiding inner product encryption scheme. Using our construction, encryption and decryption operations for vectors of length 50 complete in a tenth of a second in a standard desktop environment.
For the entire collection see [Zbl 1397.94004].