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Index calculus in the trace zero variety

Abstract : 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.
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https://hal.inria.fr/hal-01097427
Contributor : Maike Massierer <>
Submitted on : Saturday, December 26, 2015 - 3:28:55 PM
Last modification on : Wednesday, November 28, 2018 - 2:48:22 PM
Long-term archiving on: : Sunday, March 27, 2016 - 10:40:41 AM

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Elisa Gorla, Maike Massierer. Index calculus in the trace zero variety. Advances in Mathematics of Communications, AIMS, 2015, 9 (4), pp.515--539. ⟨10.3934/amc.2015.9.515⟩. ⟨hal-01097427v2⟩

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