• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.303-309
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• 2009

Cryptographic protocols depend on the hardness of some computational problems for their security. Joux briefly summarized known relations between assumptions related bilinear map in a sense that if one problem can be solved easily, then another problem can be solved within a polynomial time [6]. In this paper, we investigate additional relations between them. Firstly, we show that the computational Diffie-Hellman assumption implies the bilinear Diffie-Hellman assumption or the general inversion assumption. Secondly, we show that a cryptographic useful self-bilinear map does not exist. If a self-bilinear map exists, it might be used as a building block for several cryptographic applications such as a multilinear map. As a corollary, we show that a fixed inversion of a bilinear map with homomorphic property is impossible. Finally, we remark that a self-bilinear map proposed in [7] is not essentially self-bilinear.

• Journal of KIISE:Computer Systems and Theory
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• v.32 no.1
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• pp.1-8
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• 2005

Image morphing to generate 2D transitions between images may be difficult even to express simple 3D transformations. In addition, previous view morphing method requires control points for postwarping, and is much affected by self- occlusion. This paper presents a new morphing algorithm that can generate automatically in-between scenes from un-calibrated images. Our algorithm rectifies input images based on the fundamental matrix, which is followed by linear interpolation with bilinear disparity map. In final, we generate in-between views by inverse mapping of homography between the rectified images. The proposed method nay be applied to photographs and drawings, because neither knowledge of 3D shape nor camera calibration, which is complex process generally, is required. The generated in-between views can be used in various application areas such as simulation system of virtual environment and image communication.