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Computing $\varphi(N)$ for an RSA module with a single quantum query (2406.04061v3)
Published 6 Jun 2024 in cs.CR and quant-ph
Abstract: 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 $1-\frac{C}{N{1/2}}$.