我们在随机预言模型下给出了方案的安全性证明。
The formal security proof of this scheme is provided in the random oracle model.
我们证明该方案在随机预言机模型中是可证安全的。
Then we prove that our scheme satisfies these security notions in the random oracle model.
最后，在随机预言机模型下给出了协议的安全性分析。
On the other hand, the solution retains the tree structure. At the last, we give a security analysis based on the random oracle security model.
该方案在离散对数问题和随机预言模型假设下是安全的。
The scheme is secure under the assumption of the intractability of logarithm problems and the random oracle model.
证明了在BDH问题假设和随机预言机下新方案是安全的。
It is proved that the proposed scheme is secure under the BDH assumption and the random oracle model.
与随机预言模型中的协议相比，在计算和通信效率方面相当。
Compared with the protocol in the random oracle model, the protocol has the same computational and communication efficiencies.
最后，在随机预言模型和理想密码模型中证明了协议的安全性。
It is based on the protocol of Burmester and Desmedt and is provably-secure in the random-oracle and ideal-cipher models.
在随机预言模型下，该方案在适应性选择密文攻击下是可证明安全的。
In the random oracle model, the scheme is provably secure against adaptive chosen ciphertext attacks.
作为短签名时，签名是一次性的，该方案的安全性证明不需要随机预言机模型。
The security of the scheme is based on the difficulty of integers factorization without the random oracle model.
在随机预言模型下，可证明该方案在适应性选择消息攻击下是存在不可伪造的。
It is proven to be existential unforgeable against chosen message attack under the random oracle model.
该方案在随机预言模型下是可证明安全的，而且也是高效的方案，只需要一个对运算。
The scheme is provably secure in the random oracle model, and is an efficient scheme. It only needs one pairing operation.
安全性分析表明，在假设CDH问题是难解的情况下，该方案在随机预言模型中是可证安全的。
The performance analysis results show that the scheme is provably secure in the random oracle model under the CDH problem assumption.
采用随机预言机模型，分析了新方案的安全性，结果表明，新方案满足不可伪造性和部分盲性。
The security of the new scheme was analyzed with the random oracle model. The results show that the new scheme satisfies the unforgeability and the partial blindness.
证明了在随机预言模型中给出的协议是零知识交互证明，并显示出通过参数的适当选取，此方案比j。
It is proved that the given protocol is a zero-knowledge interactive proof in the random oracle model, and it is shown that the scheme is more secure than the scheme of J.
然后用该模型分析了一个具体的代理签名体制的例子，证明了这个代理签名方案在随机预言模型下是可证安全的。
Then, we present an examples of proxy signature scheme that can be proven secure in the random oracle model respectively.
倘若用科学假设的眼光来看，宗教信仰的确不值一提：他们仅仅讨论一些特例，他们都是随机事件，他们很少做出预测并且就算他们给出了一些预言，也很少成为现实。
Taken as hypotheses, religious claims do very badly: they are ad hoc, they are arbitrary, they rarely make predictions and when they do they almost never come true.
倘若用科学假设的眼光来看，宗教信仰的确不值一提：他们仅仅讨论一些特例，他们都是随机事件，他们很少做出预测并且就算他们给出了一些预言，也很少成为现实。
Taken as hypotheses, religious claims do very badly: they are ad hoc, they are arbitrary, they rarely make predictions and when they do they almost never come true.
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