JSIAM Letters
Online ISSN : 1883-0617
Print ISSN : 1883-0609
ISSN-L : 1883-0617
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An experiment of number field sieve for discrete logarithm problem over $\text{GF}(p^n)$
Kenichiro HayasakaKazumaro AokiTetsutaro KobayashiTsuyoshi Takagi
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2014 Volume 6 Pages 53-56

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Abstract

The security of the optimal Ate pairing using the BN curves is based on the hardness of the DLP over $\text{GF}(p^{12})$. At CRYPTO 2006, Joux et al. proposed the number field sieve over $\text{GF}(p^n)$, but the number field sieve needs multi-dimensional sieving. In this paper, we deal with the multi-dimensional sieving, and discuss its parameter sizes such as the dimension of sieving and the size of the sieving region from some experiments of the multi-dimensional sieving. Using efficient parameters, we have solved the DLP over $\text{GF}(p^{12})$ of 203 bits in about 43 hours using a PC of 16 CPU cores.

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© 2014, The Japan Society for Industrial and Applied Mathematics
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