This paper revisits the issue of obtaining KGC (Key Generator Center) trust level 3 in certificateless cryptography. The AP (Al-Riyami-Paterson) binding technique can modularly construct the certificateless encryption/signature scheme with trust level 3 from that with trust level 2. However, its security proof has been an open problem. Yang and Tan improved the AP framework by adding extra cryptographic tools: random oracles for security proof in the random oracle model or trapdoor hash functions for security proof in the standard model. This paper aims to prove secure the original AP binding technique. The basic technique for achieving this security proof depends on the improved security model for certificateless encryption (or signature) schemes. As an application example, one key dependent certificateless encryption scheme with both authority trust level 3 and provable security in the standard model is modularly constructed by applying the AP binding framework to one conventional certificateless encryption scheme.
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