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- W2893614166 abstract "Since 2013 there have been several developments in algorithms for computing discrete logarithms in small-characteristic finite fields, culminating in a quasi-polynomial algorithm. In this paper, we report on our successful computation of discrete logarithms in the cryptographically-interesting characteristic-three finite field $mathbb{F}_{3^{6.509}}$ using these new algorithms; prior to 2013, it was believed that this field enjoyed a security level of 128 bits. We also show that a recent idea of Guillevic can be used to compute discrete logarithms in the cryptographically-interesting finite field $mathbb{F}_{3^{6.709}}$ using essentially the same resources as we expended on the $mathbb{F}_{3^{6.509}}$ computation. Finally, we argue that discrete logarithms in the finite field $mathbb{F}_{3^{6.1429}}$ can feasibly be computed today; this is significant because this cryptographically-interesting field was previously believed to enjoy a security level of 192 bits." @default.
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- W2893614166 date "2018-01-01" @default.
- W2893614166 modified "2023-10-05" @default.
- W2893614166 title "Computing discrete logarithms in cryptographically-interesting characteristic-three finite fields" @default.
- W2893614166 doi "https://doi.org/10.3934/amc.2018044" @default.
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