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Provable Security is a formal method for proving the security of cryptographic schemes, in which the difficulty of breaking a particular scheme is formally related to that of solving a widely believed computational hard problem. Provable security has already become an important theme of theoretical researches in modern cryptography. This dissertation investigates the provable security of public-key encryptions and hybrid encryptions of asymmetric and symmetric encryptions. This includes the various formal security notions and the constructions can be proved to achieve them. Among the constructions, hybrid encryptions are themselves an important way to obtain public-key encryption schemes with chosen ciphertext security. The main results are as follows:(1) The one-wayness of the trapdoor one-way function in NTRU depends on the randomness of the session key, which is different from previous ones. Based on this observation, a new kind of trapdoor one-way function, trapdoor one-way functions with an auxiliary random variable is proposed.

可证明安全性是一种证明密码学方案安全性的形式化方法，它将密码学方案的安全性归约为公认的计算难题，已成为现代密码学领域中理论工作的主线，本文主要研究公钥加密与单双钥混合加密的可证明安全性，这包括它们的各种形式化安全性定义以及达到这些安全性定义的方案构造，而单双钥混合加密本身也是一种构造选择密文安全公钥加密的重要方法，本文得到的主要结果如下：(1)在研究NTRU公钥加密的特殊性基础上，对于公钥加密的陷门单向函数加密模型进行了扩展，提出了具有辅助陷门单向函数的概念，并将其扩展到多元的情况，讨论了可能的密码学用途。

This particular specimen appears to be a weak Unholy Avenger.

这个独特的物件看来是一柄脆弱的不洁的复仇者。

In particular, significant development can be seen in the average term of expected education.

但是既存在着城乡、地区之间的不平衡。

Employee criterion averment says afore-mentioned Baidu: This is new media characteristic, be not the problem with particular Baidu, portal website also is put in similar operation.

上述百度员工则申辩说：这是新媒体特色，并非百度独有的问题，门户网站也存在类似操作。

I have a particular aversion / dislike .....

我特别不喜欢。。。

I have a particular aversion to fishing.

我超不喜欢钓鱼的。

I have a particular aversion of fishing.

我特别不喜欢钓鱼。

I have a particular aversion to dancing.

我特别喜欢跳舞。

I have a particular aversion to fishing....

不明白为什么要用a。。。。。有人解释吗？

I have a particular aversion to noise.

我对噪音特别反感。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。