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I am reading in literature articles and journals about Super Elliptic Curves and Super Singular Elliptic Curves such as this: https://arxiv.org/pdf/1906.02373

I have 2 questions:

  1. Do Super Elliptic Curves have anything to do with Hyper Elliptic Curves?
  2. Can we use Super/Super-Singular Elliptic Curves in Cryptography? If yes, why there is not any known commercial approach?
someone
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1 Answers1

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Supersingular curves have weaknesses and thus are not used in Elliptic Curve Cryptography. This has been known for a long time, see for example, the statement in the PhD thesis on page 11, available here ($\ell$ is the order of the generator):

the embedding degree of $E$ (i.e., the order of $p \in \mathbb{F}^*$ if $\ell$ is prime) should be large enough (e.g., at least $20$ for the current parameter sizes), otherwise the MOV attack based on multiplicative transfer using the Weil and Tate pairings applies [Sem96; FR94; MOV93] - in particular, this rules out all super singular curves;

If one uses much larger base-field sizes as pointed out in the comments then this negates the efficiency gains of ECC. At the same time, the application to constructing pairing-friendly curves is a plus.

kodlu
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