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 $1-\frac{C\log\log N}{N^{1/2}}$.

翻译：本文提出一种多项式时间算法，通过输入随机选取整数模$N$的阶，计算RSA模数$N$的$\varphi(N)$值。该算法仅需执行一次最大公约数计算、两次乘法和一次除法运算。算法以至少$1-\frac{C\log\log N}{N^{1/2}}$的概率成功运行。