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In this paper, firstly, the authors introduce a new security definition called secret key awareness security which is to guarantee anyone generating the public key to know the corresponding secret key. Following, they give a concrete implementing for secret key awareness security. Secondly, they present two applications: one is in plaintext awareness security cryptosystem, and another is in certificatless public key encryption scheme. For encryption scheme, a variety of goals including INDistinguishability (IND), Non-Malleability (NM) and Plaintext Awareness (PA) have been introduced which are actually stronger than the notion.
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