Computing $\varphi(N)$ for an RSA module with a single quantum query
<|reference_start|>Computing $\varphi(N)$ for an RSA module with a single quantum query: 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 $1-\frac{C}{N^{1/2}}$.<|reference_end|>
@article{dieulefait2024computing,
    title={Computing $\varphi(N)$ for an RSA module with a single quantum query},
    author={Luis V'ictor Dieulefait, Jorge Urr'oz},
    journal={arXiv preprint arXiv:2406.04061},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.04061},
    primaryClass={cs.CR quant-ph}
}