The tate pairing and the discrete logarithm applied to elliptic curve cryptosystems

IEEE Transactions on Information Theory

Volumn 45, Issue 5, 1999, Pages 1717-1719

  Frey, Gerhard ^a   Müller, Michael ^a   Rück, Hans Georg ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

Cryptography; Discrete logarithm; Elliptic curves; Tate pairing

Indexed keywords

ALGEBRA; ALGORITHMS; COMPUTATIONAL GEOMETRY; CRYPTOGRAPHY; PROBABILITY;

DISCRETE LOGARITHM; ELLIPTIC CURVE CRYPTOSYSTEMS; TATE PAIRING;

INFORMATION THEORY;

EID: 0032649638     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.771254     Document Type: Article

References (7)

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3. A. Menezes, T. Okamoto, and S. A. Vanstone, "Reducing elliptic curve logarithms to logarithms in a finite field," IEEE Trans. Inform. Theory, vol. 39, pp. 1639-1646, 1993.
4. V. Miller, "Short programs for function on curves," unpublished, 1996.
5. H. G. Rück, "On the discrete logarithm in the divisor class group of curves," Math. Comput., to be published.
6. I. A. Semaev, "Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p," Math. Comput., vol. 67, pp. 353-356, 1998.
7. J. H. Silverman, Arithmetic of Elliptic Curves, GTM 106. Heidelberg, Germany: Springer-Verlag, 1986.