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Targeted Fully Homomorphic Encryption Based on a Double Decryption Algorithm for Polynomials

Tsinghua Science and Technology 2014年第5期19卷 478-485页

作者： Yatao Yang Shuang Zhang Junming Yang Jia Li Zichen Li Beijing Electronic Science and Technology Institute Communication Engineering Institute Xidian University

Several public-key encryption schemes used to solve the problem of ciphertext data processing on the fly are discussed. A new targeted fully homomorphic encryption scheme based on the discrete logarithm problem is presented. Public-key encryption cryptosystems are classified to examine homomorphic encryption. Without employing techniques proposed by Gentry such as somewhat homomorphic and bootstrapping techniques, or relinearization technique proposed by Brakerski et al., a new method called ＂Double Decryption Algorithm＂ is employed in our cryptography to satisfy a fully or targeted fully homomorphic property. Inspired by EIGamal and BGN cryptography, we obtain the desired fully homomorphic property by selecting a new group and adding an extra component to the ciphertext. Proof of semantic security is also demonstrated.

关键词： targeted fully homomorphic encryption discrete logarithm problem exponential function method power function method

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Joint Rock Coefficient Estimation Based on Hausdorff Dimension

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Advances in Pure Mathematics 2017年第11期7卷 615-640页

作者： Dalibor Martisek Institute of Mathematics Faculty of Mechanical Engineering Brno University of Technology Brno Czech Republic

The strength of rock structures strongly depends inter alia on surface irregularities of rock joints. These irregularities are characterized by a coefficient of joint roughness. For its estimation, visual comparison is often used. This is rather a subjective method, therefore, fully computerized image recognition procedures were proposed. However, many of them contain imperfections, some of them even mathematical nonsenses and their application can be very dangerous in technical practice. In this paper, we recommend mathematically correct method of fully automatic estimation of the joint roughness coefficient. This method requires only the Barton profiles as a standard.

关键词： Hausdorff Dimension Self-Similarity Self-Affinity Box Counting method power function method Barton Profile JRC Index

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