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CertificateLess public key Encryption (CLE) and Certificate Based Encryption (CBE) are two novel public key cryptographic primitives requiring no authenticity verification of the recipient's public key. Both of them are motivated to simultaneously solve the heavy certificate management problem inherent in the traditional Public Key Encryption (PKE) and the key escrow problem inherent in the Identity-Based Encryption (IBE). It is an attractive cryptographic task to formally explore the relation between CBE and CLE. In 2005, Al-Riyami and Paterson proposed one general conversion from CLE to CBE.
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