F4 Traces and Index Calculus on Elliptic Curves Over Extension Fields

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Microsoft Research
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Published on ● Video Link: https://www.youtube.com/watch?v=w0q4rG49lfk


Duration: 58:13
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Recently, Gaudry and Diem have proposed an index calculus method for the resolution of the DLP on elliptic curves defined over extension fields. In this talk, I will first present a variant of this method that enables to decrease the asymptotic complexity of the DLP on E(Fqn) for a large range of q and n, then introduce a second improvement provided by the use of F4 traces for polynomial system solving. Finally, I will give a practical example of our index calculus variant to the oracle-assisted Static Diffie-Hellman Problem. This is a joint work with Antoine Joux.



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