The discrete logarithm problem is analyzed from the perspective of Tate local duality. Local duality in the multiplicative case and the case of Jacobians of curves over p-adic local fields are considered. When the loc...The discrete logarithm problem is analyzed from the perspective of Tate local duality. 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 does not contains the necessary roots of unity, similar results can be obtained at the cost of going to an extension that contains these roots of unity. There was evidence in the analysis that suggests that the minimal extension where the local duality can be rationally and algorithmically defined must contain the roots of unity. Therefore, the discrete logarithm problem appears to be well protected against an attack using local duality. These results are also of independent interest for algorithmic study of arithmetic duality as they explicitly relate local duality in the case of curves over local fields to the multiplicative case and Tate-Lichtenbaum pairing (over finite fields).展开更多
Quark-hadron duality of three proton spin structure functions g1, g2 and gT are discussed simultaneously. It is found that the onsets of the quark-hadron dualities of g1^p, g2^p and gT^p. are similar and they are expe...Quark-hadron duality of three proton spin structure functions g1, g2 and gT are discussed simultaneously. It is found that the onsets of the quark-hadron dualities of g1^p, g2^p and gT^p. are similar and they are expected to be at about Q2～2 GeV2. In addition, our results show that the elastic peak remarkably breaks local quark-hadron duality.展开更多
文摘The discrete logarithm problem is analyzed from the perspective of Tate local duality. 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 does not contains the necessary roots of unity, similar results can be obtained at the cost of going to an extension that contains these roots of unity. There was evidence in the analysis that suggests that the minimal extension where the local duality can be rationally and algorithmically defined must contain the roots of unity. Therefore, the discrete logarithm problem appears to be well protected against an attack using local duality. These results are also of independent interest for algorithmic study of arithmetic duality as they explicitly relate local duality in the case of curves over local fields to the multiplicative case and Tate-Lichtenbaum pairing (over finite fields).
基金Supported by the National Natural Science Foundation of China under Grant Nos 90103020 and 10475088, the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No KC2-SW-N02, and the Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator.
文摘Quark-hadron duality of three proton spin structure functions g1, g2 and gT are discussed simultaneously. It is found that the onsets of the quark-hadron dualities of g1^p, g2^p and gT^p. are similar and they are expected to be at about Q2～2 GeV2. In addition, our results show that the elastic peak remarkably breaks local quark-hadron duality.
