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The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems.

, , and . IEEE Trans. Inf. Theory, 45 (5): 1717-1719 (1999)

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Algebraic Realizations of DL Systems., and . Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman and Hall/CRC, (2005)Background on Weil Descent., and . Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman and Hall/CRC, (2005)Transfer of Discrete Logarithms., and . Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman and Hall/CRC, (2005)Background on Pairings., and . Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman and Hall/CRC, (2005)Fast Bilinear Maps from the Tate-Lichtenbaum Pairing on Hyperelliptic Curves., and . ANTS, volume 4076 of Lecture Notes in Computer Science, page 466-479. Springer, (2006)Arithmetic of Modular Curves and Applications., and . Algorithmic Algebra and Number Theory, page 11-48. Springer, (1997)The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems., , and . IEEE Trans. Inf. Theory, 45 (5): 1717-1719 (1999)Complex Multiplication., and . Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman and Hall/CRC, (2005)Background on Curves and Jacobians., and . Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman and Hall/CRC, (2005)Varieties over Special Fields., and . Handbook of Elliptic and Hyperelliptic Curve Cryptography, Chapman and Hall/CRC, (2005)