Cryptology ePrint Archive: Report 2014/318

Index calculus in the trace zero variety

Elisa Gorla and Maike Massierer

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.

Category / Keywords: public-key cryptography / elliptic curve cryptography, discrete logarithm problem, index calculus, trace zero variety

Date: received 5 May 2014, last revised 23 Feb 2015

Contact author: maike massierer at inria fr

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Version: 20150223:101055 (All versions of this report)

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