Computing φ (N) for an RSA module with a single quantum query

In this paper, we give a polynomial time algorithm to compute φ (N) φ ( N ) for an RSA module N using as input the order modulo N of a randomly chosen integer. This provides a new insight in the very important problem of factoring an RSA module with extra information. In fact, the algorithm is extremely simple and consists only on a computation of a greatest common divisor, two multiplications and a division. The algorithm works with a probability of at least 1-1N1/2-ε 1 - 1 N 1 / 2 - ϵ , where ε ϵ is any small positive constant.