Public Key Cryptography – PKC 2010

Volume 6056 of the series Lecture Notes in Computer Science pp 384-402

Functional Encryption for Inner Product: Achieving Constant-Size Ciphertexts with Adaptive Security or Support for Negation

  • Nuttapong AttrapadungAffiliated withResearch Center for Information Security, AIST
  • , Benoît LibertAffiliated withUniversité catholique de Louvain, Crypto Group


In functional encryption (FE) schemes, ciphertexts and private keys are associated with attributes and decryption is possible whenever key and ciphertext attributes are suitably related. It is known that expressive realizations can be obtained from a simple FE flavor called inner product encryption (IPE), where decryption is allowed whenever ciphertext and key attributes form orthogonal vectors. In this paper, we construct (non-anonymous) IPE systems with constant-size ciphertexts for the zero and non-zero evaluations of inner products. These schemes respectively imply an adaptively secure identity-based broadcast encryption scheme and an identity-based revocation mechanism that both feature short ciphertexts and rely on simple assumptions in prime order groups. We also introduce the notion of negated spatial encryption, which subsumes non-zero-mode IPE and can be seen as the revocation analogue of the spatial encryption primitive of Boneh and Hamburg.


Functional encryption identity-based broadcast encryption revocation efficiency