Wikipedia:Reference desk/Archives/Mathematics/2024 December 6
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December 6
[edit]Is there anything that would prevent peforming Weil Descent on binary curves of large characteristics ?
[edit]The ghs attack involve creating an hyperlliptic curve cover for a given binary curve. The reason the attack fails most of the time is the resulting genus grows exponentially relative to the curve’s degree.
We don’t hear about the attack on finite fields of large characteristics since such curves are already secure by being prime. However, I notice a few protocol relies on the discrete logarithm security on curves with 400/500 bits modulus resulting from extension fields of characteristics that are 200/245bits long.
Since the degree is most of the time equal to 3 or 2, is there anything that would prevent creating suitable hyperelliptic cover for such curves in practice ? 2A01:E0A:401:A7C0:28FE:E0C4:2F97:8E08 (talk) 12:09, 6 December 2024 (UTC)