Certificate-based Smooth Projective Hashing and Its Applications

Smooth projective hashing was firstly introduced by Cramer and Shoup (EuroCrypt’02) as a tool to construct efficient chosen-ciphertext-secure public key encryption schemes. Since then, they have found many other applications, such as password-based authenticated key exchange, oblivious transfer, zero-knowledge arguments et al. Certificate-based encryption (CBE) not only eliminates third-party queries and heavy certificate management problem in traditional public-key encryption, but also solves key escrow problem for identity-based encryption. We introduce the new concept of certificate-based smooth projective hashing (CB-SPH). Under the security model for the leakage-resilient certificate-based encryption (LR-CBE), we show how to construct a general leakage-resilient certificate-based encryption scheme using the certificate-based smooth projective hashing. Based on these theoretical constructions, we present two concrete CB-SPH instantiations under the DBDH assumption and the DLWE assumption respectively. Based on these CB-SPH instantiations, we can construct leakage resilient CBE schemes.