Cryptology ePrint Archive: Report 2008/070

Generators of Jacobians of Genus Two Curves

Christian Robenhagen Ravnshoj

Abstract: We prove that in most cases relevant to cryptography, the Frobenius endomorphism on the Jacobian of a genus two curve is represented by a diagonal matrix with respect to an appropriate basis of the subgroup of l-torsion points. From this fact we get an explicit description of the Weil-pairing on the subgroup of l-torsion points. Finally, the explicit description of the Weil-pairing provides us with an efficient, probabilistic algorithm to find generators of the subgroup of l-torsion points on the Jacobian of a genus two curve.

Category / Keywords: Jacobians, hyperelliptic genus two curves, pairings, embedding degree

Date: received 11 Feb 2008, last revised 18 Feb 2008

Contact author: cr at imf au dk

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Version: 20080218:120409 (All versions of this report)

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