- Issue 4 Pages 381-
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Ai Ishikawa, Takaharu Yaguchi2016 Volume 26 Issue 4 Pages 381-415
Published: 2016
Released on J-STAGE: December 25, 2016
JOURNAL FREE ACCESSAbstract. The discrete gradient method is a method to derive energy-conservative or-dissipative numerical schemes for Hamiltonian equations or gradient flows. This method discretizes the equation by using a discrete gradient, which is a discrete analogue of a gradient. Because a gradient and hence a discrete gradient depend on the inner product, the resultant scheme apparently depends on the underlying Riemannian structure of the space. However, when the method is applied to Hamiltonian systems it often turns out that the scheme is actually independent of the inner product. In this paper, we investigate this invariance of the discrete gradient method.
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Ryo Hiromasa, Masayuki Abe, Tatsuaki Okamoto2016 Volume 26 Issue 4 Pages 416-439
Published: 2016
Released on J-STAGE: December 25, 2016
JOURNAL FREE ACCESSAbstract. In this paper, we construct a new RSA-based signature scheme that is tightly secure in the random oracle model. The number of random oracles used in this scheme is less than that of all previous schemes with same security guarantee. We then show that for any PPT adversary there exists a concrete hash function from indistinguishability obfuscation that can replace the random oracle with keeping security. The same statement can be proven for the signatures of Coron.
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