Computing $φ(N)$ for an RSA module with a single quantum query
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866911198899863552 |
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| author | Dieulefait, Luis Víctor Urróz, Jorge |
| author_facet | Dieulefait, Luis Víctor Urróz, Jorge |
| contents | In this paper we give a polynomial time algorithm to compute $φ(N)$ 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 $1-\frac{1}{N^{1/2-ε}}$, where $ε$ is any small positive constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04061 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing $φ(N)$ for an RSA module with a single quantum query Dieulefait, Luis Víctor Urróz, Jorge Cryptography and Security Quantum Physics In this paper we give a polynomial time algorithm to compute $φ(N)$ 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 $1-\frac{1}{N^{1/2-ε}}$, where $ε$ is any small positive constant. |
| title | Computing $φ(N)$ for an RSA module with a single quantum query |
| topic | Cryptography and Security Quantum Physics |
| url | https://arxiv.org/abs/2406.04061 |