Computing $\varphi(N)$ for an RSA module with a single quantum query

• URL: http://arxiv.org/abs/2406.04061v3
• Date: Tue, 2 Jul 2024 14:14:32 GMT
• Title: Computing $\varphi(N)$ for an RSA module with a single quantum query
• Authors: Luis Víctor Dieulefait, Jorge Urróz,
• Abstract summary: We give a computation time algorithm to compute $varphi(N)$ for an RSA module $N$ using as input the order modulo $N$ of a randomly chosen integer.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $1-\frac{C}{N^{1/2}}$.

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