射线攻击，一种无效的破解RSA密码系统的尝试
The ray attack, an inefficient trial to break RSA cryptosystems
摘要：
介绍了RSA密码系统的基本性质和一些经典的攻击方法。利用欧拉函数射线的几何性质，提出了一种新的攻击RSA密码系统的方法。由此产生的，虽然效率低下，算法。它基本上由一个循环组成，该循环的起始值由欧拉函数ray确定，步长由函数$ω_e(n)$给出，该函数是$\mathrm{ord}_n(e)$阶的倍数，其中$e$表示公钥指数，$n$表示RSA模数。对于$n=pq$和较小素因子$p$的估计$r<\sqrt{pq}$，运行时间由$T(e,n,r) = O((r-p)\ln e \ln n \ln r).$给出
英文摘要：
The basic properties of RSA cryptosystems and some classical attacks on them are described. Derived from geometric properties of the Euler functions, the Euler function rays, a new ansatz to attack RSA cryptosystems is presented. A resulting, albeit inefficient, algorithm is given. It essentially consists of a loop with starting value determined by the Euler function ray and with step width given by a function $ω_e(n)$ being a multiple of the order $\mathrm{ord}_n(e)$, where $e$ denotes the public key exponent and $n$ the RSA modulus. For $n=pq$ and an estimate $r<\sqrt{pq}$ for the smaller prime factor $p$, the running time is given by $T(e,n,r) = O((r-p)\ln e \ln n \ln r).$
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