Feb. 8, 2024, 5:10 a.m. | Oisin Robinson

cs.CR updates on arXiv.org arxiv.org

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 …

bits box collecting computation cs.cr implementation medium record report size

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