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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2212.04999 |
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- We report on an implementation of the Extended Tower Number Field Sieve (ExTNFS) and record computation in a medium characteristic finite field $\mathbb{F}_{p^4}$ of 512 bits size. Empirically, we show that sieving in a 4-dimensional box (orthotope) for collecting relations for ExTNFS in $\mathbb{F}_{p^4}$ is faster than sieving in a 4-dimensional hypersphere. We also give a new intermediate descent method, `descent using random vectors', without which the descent stage in our ExTNFS computation would have been difficult/impossible, and analyze its complexity.