关键词: DCR假设, KDM安全性, CCA安全性, 公钥加密, Cramer-Shoup方案

Abstract: The definition of KDM （Key-Dependent Message） security is related to some specific ensemble[F]. By introducing a new ensemble of functions, it proves that, in two user cases, the DCR-based scheme proposed by Cramer and Shoup is KDM-CCA secure w.r.t. the new ensemble. Since the CS-DCR scheme is very efficient, an encryption scheme is gotten which is not only somewhat KDM-CCA secure but also very efficient.

Key words: Decisional Composite Residuosity（DCR） assumption, Key-Dependent Message（KDM） security, Chosen Ciphertext Attack（CCA） security, public key encryption, Cramer-Shoup scheme