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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。

Stamp one's feet and beat one's breast; stamp one's feet and pound one's chest

成语用脚跺地，以拳捶胸。形容极度悲痛或恼怒，到了极点。

Put simply, this means that one has to know that something exists before one knows what it is, and before one knows that something exists, one has to accept that anything exists.

简单来说，这意味着一个人必须知道的东西存在，才知道它是什么，以及前一个知道的东西存在，一个人必须接受任何存在。

Having one kind of sound is inaudible , having one kind of language is to be able to not blaspheme , has one kind to feel that being to have no words to express , having one kind of strength is inexorable ......

有一种声音是听不见的，有一种语言是不能亵渎的，有一种感觉是无法描述的，有一种力量是不可抗拒的。。。。。。

Bearing consists of two thermometers, one mounted on a board used to measure oil temperature, oil spill, and the other one installed in the bearing body, the one used in tile temperature monitoring, and the other one for the alarm.

轴承共设2只温度计，其中1只装在溢油板上用于测油温，另1只装在轴承体上，1只用于瓦温监测，另1只用于报警。

Place classic playing cards on the board following one simple rule: place cards next to another one with a value of one less or one greater, regardless of the suit.

地方经典纸牌在董事会下面的一个简单的规则：卡的地方，旁边的另一位与价值，少了一个或一个更大的，不论诉讼。

Theirs are conversions not from one body plan to another, or from one organ or tissue or cell type to another, or even from one protein molecule or gene to another, but rather from one binding site to another.

生命体内的变化并不是整个身体的变化，也不是器官、组织、细胞类型从一个到另一个的变化，甚至不是蛋白质分子或基因之间的变化，而是从基因的一个结合位点到另一个结合位点的变化。

Where groups break up into sections, as they tend to do, and live apart from one another, the sections are found, though of one blood, and originally of one language, soon to speak dialects so different that they cannot understand one another.

什么地方人群象他们倾向于做的那样分成支系，并且彼此分离居住，支系就被发现，即使属于同一血统，并源于同一语言，很快就说着如此不同的方言以至彼此不能理解。

China's university students and the just sit watching one after another clumsy lies repeated thousands times, it seems that we must become truth; pouring a pot of dirty water and wantonly throwing to our motherland, and damage China's international reputation; one by one the bad guys, rebels of colluding in cahoots, there is no shame and humiliation in front of the whole world their ancestors; one after another anti-China groups feel under the banner of "human rights,""freedom" and "democracy" banner, with shameless lies and brutal violence, wanton insult to the five-star red flag, and insulted the Chinese nation!

我们中国的大学生，眼睁睁的看着一个又一个的拙劣谎言重复上千遍，似乎就要变成真理；一盆又一盆的脏水肆无忌惮地泼向我们的祖国，损坏中国国际声望；一个又一个的华奸、叛匪沆瀣一气、狼狈为奸，毫无羞耻地在世人面前羞辱自己的先祖；一个又一个的反华集团觉打着"人权"、"自由"、"民主"的旗号，用无耻的谎言和野蛮的暴力，肆意侮辱五星红旗、侮辱中华民族！

The cinema is very bad to search, put a half to give breakdown to go back replay... need memory ability remembers gut, it is a common Hollywood is big so, do not understand why to so much person can buy the ticket of 150, do so that be like ~~~ to appreciate Shanghai one week with Culture Revolution, the Sun Ganlou that still has Shuai Shuai and the film review after all editor ~~~ are small salon, be present possibly mix with respect to me wild goose is not liberal art one's previous experience, they have the blueness that nod anger literary cell, saying is almost,"I feel this film not up to much "... so that Xiang Siwei needs authority later,those who who likes this movie look in light of raise one's hand... wild goose likes 3D, apparent love hate is trenchant, touch field, vigorous speech so " reader "(she is raise one's hand, the 囧 that does not need an editor to call-over), it is this ask her to see a stage play again.

影院很不好找，放了一半出了故障倒回往重放……需要回忆才能想起剧情，所以就是部普通的好莱坞***，不懂为何会有那么多人往买150的票，搞得跟***似~~~感谢上海壹周，还有帅帅的孙甘露及所有编辑~~~之后的影评小沙龙，可能在座的就我和大雁不是文科出身，他们都有点愤青文艺细胞，说起来几乎都是，"我觉得这电影不怎么样"……以至于项斯薇后来需要大家举手来看看有谁喜欢这部电影的……大雁喜欢3D，很明显的爱恨分明，如此碰场、积极发言的"读者"（她是举手的，不需要编辑点名的囧），是该再请她往看话剧了。

Hanna: That's over now, isn't it?

都结束了，对吗

You must be ill. You look so pale.

你一定是病了，你的脸色苍白。