Topics in Cryptology – CT-RSA 2004

Volume 2964 of the series Lecture Notes in Computer Science pp 366-386

Weak Fields for ECC

  • Alfred MenezesAffiliated withUniversity of Waterloo
  • , Edlyn TeskeAffiliated withUniversity of Waterloo
  • , Annegret WengAffiliated withUniversity of Essen

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We demonstrate that some finite fields, including \(\mathbb{F}_{{2}^{210}}\), 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.