Abstract
It is shown that the computational complexity of Tate local duality is closely related to that of the discrete logarithm problem over finite fields. Local duality in the multiplicative case and the case of Jacobians of curves over p-adic local fields are considered. When the local field contains the necessary roots of unity, the case of curves over local fields is polynomial time reducible to the multiplicative case, and the multiplicative case is polynomial time equivalent to computing discrete logarithm in finite fields. When the local field dose not contains the necessary roots of unity, similar results can be obtained at the cost of going to an extension that does contain these roots of unity.
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Huang, MD. (2011). Local Duality and the Discrete Logarithm Problem. In: Chee, Y.M., et al. Coding and Cryptology. IWCC 2011. Lecture Notes in Computer Science, vol 6639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20901-7_13
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DOI: https://doi.org/10.1007/978-3-642-20901-7_13
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