Quantum attribute-based encryption: a comprehensive study

In this work, we study quantum versions of attribute-based encryption schemes. Attribute-based encryption enables fine-grained access control of encrypted data using authorization policies. The secret key of a user and the ciphertext are dependent upon attributes, and the decryption of a ciphertext is possible only if the set of attributes of the user key matches the attributes of the ciphertext. Most of the existing classical attribute-based schemes are based on the hardness of the bilinear Diffie–Hellman problem, which has been proven to be vulnerable against Shor’s algorithm. No efficient quantum attribute-based encryption scheme has been reported till date. In this backdrop, we propose quantum attribute-based encryption schemes exploiting quantum key distribution and quantum error-correcting codes. Attribute-based scheme is a special case of a more general functional encryption scheme whose quantum version we consider next hence giving this work a unifying framework. We present two constructions of quantum functional encryption schemes. The first construction generalizes the traditional notion of functional encryption and can handle multiple functions. The second construction utilizes the quantum query complexities of different Boolean functions. As applications, we present a quantum progressive functional encryption scheme to suitably encrypt an image to be shared among data users with hierarchical relations between them and outline a connection between quantum functional encryption schemes and obfuscated quantum states. In this work, we use weak measurements, which help us to expand our horizon to include encryption schemes in the dishonest model and quantum communication in the presence of an adversary. Our methods are unconditional and do not depend on the known difficulty of problems like lattice-based problems. Finally, we discuss various advantages of our methods and results.