公钥密码方案的可证明安全性注记

Remark on provable security of public key cryptographic schemes

长期以来,人们对于可证明安全的认识存在着一些误区:可证明安全的方案一定是安全的,归约证明紧的一定比归约松的更安全。总结了与方案安全性有关的几个要素,分析了公钥密码方案可证明安全的实质,纠正了以往的一些错误认识,指出可证明安全的方案不一定是安全的,归约紧的方案不一定比归约松的更安全。方案的安全性要综合四个要素一起考虑,总的来说,攻击模型越难,攻击目标越容易,困难问题越难,而归约证明最紧的方案越安全。

Provable security was a hot topic of cryptography in recent years. People have proposed many provably secure cryptographic schemes. It makes great progress compare to informal analysis and proves the security of schemes to a certain extent. However, a lot of people believe that provably secure schemes must be secure and the schemes having a tighter reduction proof are more secure than those having loose reduction. The paper generalized several factors of security, analyzed the essence of provable security about public key cryptographic schemes, rectified some wrong opinions and pointed out that provably secure scheme were not always secure and the schemes having a tighter reduction were not always more secure than that having loose reduction. The security of scheme relies on four factors. In a word, the scheme is more secure if it has a more difficult attack model, an easier secure goal, a more difficult problem and a tighter reduction proof.