Cryptology ePrint Archive: Report 2006/128

On the existence of distortion maps on ordinary elliptic curves

Denis Charles

Abstract: Distortion maps allow one to solve the Decision Diffie-Hellman problem on subgroups of points on an elliptic curve. In the case of ordinary elliptic curves over finite fields, it is known that in most cases there are no distortion maps for the Frobenius eigenspaces. In this article we characterize the existence of distortion maps in the remaining cases.

Category / Keywords: Elliptic curves, Decision Diffie-Hellman problem, Distortion maps

Date: received 30 Mar 2006, last revised 15 Aug 2006

Contact author: cdx at microsoft com

Available formats: PDF | BibTeX Citation

Note: Updated version, corrects an error in the previous proof.

Version: 20060815:224200 (All versions of this report)

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