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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。

The most important development in mathematical logic for the philosophy of mathematics was Godel's proof that any axiomatic system powerful enough to formalise arithmetic will be incomplete in the sense that there will be truths which are not provable within the system.

数理逻辑中最重要的数学哲学的发展是哥德尔的证明,任何公理系统足够强大以正式算术将在这个意义上不完全会有真理不属于系统内证明的。

The validity of the provable security of counter with cipher block chaining message authentication code mode and cipher-based message authentication code mode was studied and proved. The illustrations of different communications' encryption have been developed.

对分组密码算法CCM、CMAC加密模式进行描述,用可证安全性理论对它们进行相关研究和证明,并对各种证明情况在不同通信环境下的使用作出说明。

We also presents a suite of composable and integrated fair exchange protocols from both practicity and provable security.

还对分布式密码的应用"公平数据交换协议"进行了形式化分析和深入研究。

Keywords: distributed cryptography; provable security; composable security; threshold cryptography; secure multiparty computation

中文关键词:分布式密码;可证安全性;组合安全性;门限密码;安全多方计算

They wanted to be able to distil the problem down to a few general, provable rules that avoid exact calculations, and that work every time for any circular pizza.

他们希望能够把这一问题的实质归纳成几条普遍的、可证明的定理,以避免精确的计算,并希望只要是圆形的披萨,这些定理都适用。

So this article makes an inquiry into this issue, and author makes a conclusion that neither joinder of defendants nor injoinder of defendants confession has completely provable value.

故本文就此问题进行探讨,认为无论是同案或是异案审理的共同故意犯罪的被告人的供述均不具有完全的证据价值,不能相互补强据以定案。

Monkeys, apparently, offer one another fleas at times, but not in any provable spirit of kindliness

猴子似乎有时互相帮助捉跳蚤,但是这并不在任何可以证明的善意的范畴内。

Monkeys, apparently, offer one another flea s at times, but not in any provable spirit of kindliness

猴子似乎有时互相帮助捉跳蚤,但是这并不在任何可以证明的善意的范畴内。

The benefit is that one can build up the theory of correctness provable compiler easily.

这样处理的好处是便于构造正确性可证明的编译器设计的理论基础。

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