Cryptology ePrint Archive: Report 2018/307

Isolated Curves and the MOV Attack

Travis Scholl

Abstract: We present a variation on the CM method that produces elliptic curves over prime fields with nearly prime order that do not admit many efficiently computable isogenies. Assuming the Bateman-Horn conjecture, we prove that elliptic curves produced this way almost always have a large embedding degree, and thus are resistant to the MOV attack on the ECDLP.

Category / Keywords: public-key cryptography / elliptic curve cryptosystem, number theory

Original Publication (in the same form): Journal of Mathematical Cryptography

Date: received 30 Mar 2018

Contact author: tscholl2 at uw edu

Available format(s): PDF | BibTeX Citation

Version: 20180403:133128 (All versions of this report)

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