Cryptology ePrint Archive: Report 2003/128

Weak Fields for ECC

Alfred Menezes and Edlyn Teske and Annegret Weng

Abstract: We demonstrate that some finite fields, including GF(2^210) are weak for elliptic curve cryptography in the sense that any instance of the elliptic curve discrete logarithm problem for any elliptic curve over these fields can be solved in significantly less time than it takes Pollard's rho method to solve the hardest instances. We discuss the implications of our observations to elliptic curve cryptography, and list some open problems.

Category / Keywords: public-key cryptography /

Date: received 26 Jun 2003

Contact author: ajmeneze at uwaterloo ca

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Version: 20030627:151805 (All versions of this report)

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