Distance-Based Encryption: How to Embed Fuzziness in Biometric-Based Encryption

We introduce a new encryption notion called distance-based encryption (DBE) to apply biometrics in identity-based encryption. In this notion, a ciphertext encrypted with a vector and a threshold value can be decrypted with a private key of another vector, if and only if the distance between these two vectors is less than or equal to the threshold value. The adopted distance measurement is called Mahalanobis distance, which is a generalization of Euclidean distance. This novel distance is a useful recognition approach in the pattern recognition and image processing community. The primary application of this new encryption notion is to incorporate biometric identities, such as face, as the public identity in an identity-based encryption. In such an application, usually the input biometric identity associated with a private key will not be exactly the same as the input biometric identity in the encryption phase, even though they are from the same user. The introduced DBE addresses this problem well as the decryption condition does not require identities to be identical but having small distance. The closest encryption notion to DBE is the fuzzy identity-based encryption, but it measures biometric identities using a different distance called an overlap distance (a variant of Hamming distance) that is not widely accepted by the pattern recognition community, due to its long binary representations. In this paper, we study this new encryption notion and its constructions. We show how to generically and efficiently construct such a DBE from an inner product encryption (IPE) with reasonable size of private keys and ciphertexts. We also propose a new IPE scheme with the shortest private key to build DBE, namely, the need for a short private key. Finally, we study the encryption efficiency of DBE by splitting our IPE encryption algorithm into offline and online algorithms.