An Implementation of the Extended Tower Number Field Sieve using 4d Sieving in a Box and a Record Computation in Fp4
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914669191495680 |
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| author | Robinson, Oisin |
| author_facet | Robinson, Oisin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_04999 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An Implementation of the Extended Tower Number Field Sieve using 4d Sieving in a Box and a Record Computation in Fp4 Robinson, Oisin Cryptography and Security 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. |
| title | An Implementation of the Extended Tower Number Field Sieve using 4d Sieving in a Box and a Record Computation in Fp4 |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2212.04999 |