New explicit conditions of elliptic curve traces for FR-reduction

  title={New explicit conditions of elliptic curve traces for FR-reduction},
  author={Atsuko Miyaji and Masaki Nakabayashi and Shunzou TAKANO},
Elliptic curve cryptosystems([19],[25]) are based on the elliptic curve discrete logarithm problem(ECDLP). If elliptic curve cryptosystems avoid FRreduction([11],[17]) and anomalous elliptic curve over Fq ([3], [33], [35]), then with current knowledge we can construct elliptic curve cryptosystems over a smaller definition field. ECDLP has an interesting property that the security deeply depends on elliptic curve traces rather than definition fields, which does not occur in the case of the… CONTINUE READING
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