In this paper we give a polynomial time algorithm to compute $\varphi(N)$ for an RSA module $N$ using as input the order modulo $N$ of a randomly chosen integer. The algorithm consists only on a computation of a greatest common divisor, two multiplications and a division. The algorithm works with a probability of at least $1-\frac{C}{N^{1/2}}$.

翻译：本文提出一种多项式时间算法，用于计算RSA模数$N$的欧拉函数$\varphi(N)$。该算法以随机选取整数模$N$的阶作为输入，仅需执行一次最大公约数计算、两次乘法运算和一次除法运算即可完成。算法以至少$1-\frac{C}{N^{1/2}}$的成功概率实现目标。