Since Wiener pointed out that the RSA can be broken if the private exponent d is relatively small compared to the modulus N, it has been a general belief that the Wiener attack works for $d<N^{\frac{1}{4}}$. On the contrary, in [1], it was shown that the bound $d<N^{\frac{1}{4}}$ is not accurate as it has been thought of. Specifically, for the standard assumption of the two primes p and q that q < p < 2q, the Wiener continued fraction technique is proven to work for $d\le \frac{1}{\sqrt[4]{18}}{N}^{\frac{1}{4}}$. In this paper, we consider a general condition on the RSA primes, namely q < p < α q, and we give the corresponding bound for the Wiener attack to work, which is $d\le \frac{\sqrt[4]{\alpha }}{\sqrt{2(\alpha +1)}}{N}^{\frac{1}{4}}$. In a special case when $\alpha =2,$ this general bound agrees with the result of [1].

由于Wiener指出，如果私有指数d与模数N相比较小，则RSA可能会被破坏，因此人们普遍认为Wiener攻击适用于$d<{ñ}^{\frac{\mathrm{1个}}{4}}$。相反，在[1]中表明$d<{ñ}^{\frac{\mathrm{1个}}{4}}$正如所想到的那样不准确。具体地，对于两个素数的标准假设p和q的是q  <  p  <2 q，维纳连分数技术被证明工作$d\le \frac{\mathrm{1个}}{\sqrt[4]{18}}{ñ}^{\frac{\mathrm{1个}}{4}}$。在本文中，我们考虑对RSA素数的一般条件，即q  <  p  <  α  q，我们给出相应的约束维纳攻击工作，这是$d\le \frac{\sqrt[4]{\alpha }}{\sqrt{2（\alpha +\mathrm{1个}）}}{ñ}^{\frac{\mathrm{1个}}{4}}$。在特殊情况下$\alpha =2，$ 该一般界限与[1]的结果一致。