Reconstructing points of superelliptic curves over a prime finite field
Let p be a prime and Fp the finite field with p elements. We show how, when given an superelliptic curve Y n + f(X) ∈ Fp[X, Y ] and an approximation to (v0, v1) ∈ F2 p such that vn 1 = −f(v0), one can recover (v0, v1) efficiently, if the approximation is good enough. As consequence we provide an upp...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/31261 |
| Acceso en línea: | https://hdl.handle.net/10902/31261 |
| Access Level: | acceso abierto |
| Palabra clave: | Superelliptic curves Lattice techniques Prime finite fields Cryptography |
| Sumario: | Let p be a prime and Fp the finite field with p elements. We show how, when given an superelliptic curve Y n + f(X) ∈ Fp[X, Y ] and an approximation to (v0, v1) ∈ F2 p such that vn 1 = −f(v0), one can recover (v0, v1) efficiently, if the approximation is good enough. As consequence we provide an upper bound on the number of roots of such bivariate polynomials where the roots have certain restrictions. The results has been motivated by the predictability problem for non-linear pseudorandom number generators and, other potential applications to cryptography. |
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