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Recently, a series of works made a breakthrough to consider a postchallenge leakage. They presented achievable public key encryption (PKE) schemes which are semantically secure against after-the-fact leakage in the split-state model. This model puts a more acceptable constraint on adversary\u2019s ability that the adversary cannot query the leakage of secret states as a whole but the functions of several parts separately instead of prechallenge query only. To obtain security against chosen ciphertext attack (CCA) for PKE schemes against after-the-fact leakage attack (AFL), existing works followed the paradigm of \u201cdouble encryption\u201d which needs noninteractive zero knowledge (NIZK) proofs in the encryption algorithm. We present an alternative way to achieve AFL-CCA security via lossy trapdoor functions (LTFs) without NIZK proofs. First, we formalize the definition of LTFs secure against AFL (AFLR-LTFs) and all-but-one variants (ABO). Then, we show how to realize this primitive in the split-state model. This primitive can be used to construct AFLR-CCA secure PKE scheme in the same way as the method of \u201cCCA from LTFs\u201d in traditional sense.<\/jats:p>","DOI":"10.1155\/2019\/8357241","type":"journal-article","created":{"date-parts":[[2019,10,31]],"date-time":"2019-10-31T19:48:24Z","timestamp":1572551304000},"page":"1-8","source":"Crossref","is-referenced-by-count":1,"title":["CCA Secure Public Key Encryption against After-the-Fact Leakage without NIZK Proofs"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0553-113X","authenticated-orcid":true,"given":"Yi","family":"Zhao","sequence":"first","affiliation":[{"name":"Computer Science, Shaanxi Normal University, 710119 West Changan Street 620, Xi\u2019an, Shaanxi, China"},{"name":"State Key Laboratory of Cryptology, P.O. 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