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The paper proposes a HIBE scheme, which improves upon Waters' scheme from Eurocrypt 2005 by significantly reducing the size of the public parameters. The improvement is based on two ideas: 1 partitioning the identities in smaller blocks; 2 reusing public parameters. Modification of the basic HIBE scheme yields a CCA-secure hybrid HIBE where symmetric key authentication is used to eliminate costly pairing operations from the decryption algorithm. The protocols and the security arguments are recast in the most efficient asymmetric pairing setting where one gets several variants of the basic protocol with associated trade-offs in the ciphertext overhead and public parameter size. For practical security levels, the variants we obtain are currently the most efficient and practical among all other schemes which achieve similar security under the DBDH assumption. The basic idea provides improvements to the construction of other cryptographic primitives such as signatures, wildcard IBE and certificateless encryption.

Practical hybrid (hierarchical) identity-based encryption schemes based on the decisional bilinear Diffie-Hellman assumption