标准模型下可证明安全的新公钥加密方案

摘要

针对标准模型下抗适应性选择密文攻击语义安全的公钥加密方案存在的效率比较低或者所基于的计算假设比较强的问题,基于最近提出的d-判定性Diffie-Hellman问题构造了一个新的可证明安全的公钥加密方案.方案的构造和安全性证明采用哈希证明系统方法,达到了高效安全的目标.方案所基于的d-判定性Diffie-Hellman问题的难度介于计算Diffie-Hellman问题和判定性Diffie-Hellman问题之间,方案的效率优于基于计算Diffie-Hellman问题的方案,与基于判定性Diffie-Hellman问题的方案相近.该方案实现了计算假设与效率之间的一个比较好的折中,并且可以根据实际需要选择不同的d值以达到不同的安全级别.%The public key encryption schemes with semantic security against adaptively chosen cipertext attacks in the standard model suffer from the drawbacks of low efficiency or strong computational assumptions. Concerning these problems, a new provable secure public key encryption scheme was proposed based on the newly introduced d-decisional Diffie-Hellman problem. To obtain the security and efficiency, the methodology of Hash proof system was adopted in the construction and security proof of the scheme. The intractability of the d-decisional Diffie-Hellman problem was between that of the computational Diffie-Hellman problem and decisional Diffie-Hellman problem. The efficiency of the scheme surpassed that of the schemes based on the computational Diffie-Hellman problem and approximated with the schemes based on the deeisional Diffie-Hellman problem. Therefore, the proposed scheme has reached a good compromise between efficiency and computational assumption. Moreover, it can select different d for different security demand of applications.