Index calculus in the trace zero variety
Elisa Gorla Maike Massierer
We discuss how to apply Gaudry's index calculus algorithm for abelian varieties to solve the discrete logarithm problem in the trace zero variety of an elliptic curve. We treat in particular the practically relevant cases of field extensions of degree 3 or 5. Our theoretical analysis is compared to other algorithms present in the literature, and is complemented by results from a prototype implementation.
keywords: trace zero variety. index calculus discrete logarithm problem Elliptic curve cryptography

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