Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iter...Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.展开更多
In this paper, we study the RSA public key cryptosystem in a special case with the private exponent d larger than the public exponent e. When N^0.258 ≤ e ≤N^0.854, d 〉 e and satisfies the given conditions, we can p...In this paper, we study the RSA public key cryptosystem in a special case with the private exponent d larger than the public exponent e. When N^0.258 ≤ e ≤N^0.854, d 〉 e and satisfies the given conditions, we can perform cryptanalytic attacks based on the LLL lattice basis reduction algorithm. The idea is an extension of Boneh and Durfee＇s researches on low private key RSA, and provides a new solution to finding weak keys in RSA cryptosystems.展开更多
Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. Ho...Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. However, one problem arises here that if the equation has a short solution in given bounded range, the results outputted by earlier algorithms are often not the ones we are interested in. In this paper, we present a probability method based on lattice basis reduction to solve the problem. For a general multivariate modular linear equation with short solution in the given bounded range, the new method outputs this short solution in polynomial time, with a high probability. When the number of unknowns is not too large （smaller than 68）, the probability is approximating 1. Experimental results show that Knapsack systems and Lu-Lee type systems are easily broken in polynomial time with this new method.展开更多
基金funded by the NSFC under Grant Nos.61803279,71471091,62003231 and 51874205in part by the Qing Lan Project of Jiangsu,in part by the China Postdoctoral Science Foundation under Grant Nos.2020M671596 and 2021M692369+2 种基金in part by the Suzhou Science and Technology Development Plan Project(Key Industry Technology Innovation)under Grant No.SYG202114in part by the Natural Science Foundation of Jiangsu Province under Grant No.BK20200989Postdoctoral Research Funding Program of Jiangsu Province.
文摘Discrete Tomography(DT)is a technology that uses image projection to reconstruct images.Its reconstruction problem,especially the binary image(0–1matrix)has attracted strong attention.In this study,a fixed point iterative method of integer programming based on intelligent optimization is proposed to optimize the reconstructedmodel.The solution process can be divided into two procedures.First,the DT problem is reformulated into a polyhedron judgment problembased on lattice basis reduction.Second,the fixed-point iterativemethod of Dang and Ye is used to judge whether an integer point exists in the polyhedron of the previous program.All the programs involved in this study are written in MATLAB.The final experimental data show that this method is obviously better than the branch and bound method in terms of computational efficiency,especially in the case of high dimension.The branch and bound method requires more branch operations and takes a long time.It also needs to store a large number of leaf node boundaries and the corresponding consumptionmatrix,which occupies a largememory space.
基金Supported partially by the National Basic Research Program of China (Grant No. 2003CB314805)the National Natural Science Foundationof China (Grant Nos. 90304014 and 60873249)the Project funded by Basic Research Foundation of School of Information Science and Technology of Tsinghua
文摘In this paper, we study the RSA public key cryptosystem in a special case with the private exponent d larger than the public exponent e. When N^0.258 ≤ e ≤N^0.854, d 〉 e and satisfies the given conditions, we can perform cryptanalytic attacks based on the LLL lattice basis reduction algorithm. The idea is an extension of Boneh and Durfee＇s researches on low private key RSA, and provides a new solution to finding weak keys in RSA cryptosystems.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60873249, 60973142)the National High-Tech Research & Development Program of China (Grant Nos. 2008AA10Z419, 2009AA011906)the Project Funded by Basic Research Foundation of School of Information Science and Technology of Tsinghua University
文摘Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. However, one problem arises here that if the equation has a short solution in given bounded range, the results outputted by earlier algorithms are often not the ones we are interested in. In this paper, we present a probability method based on lattice basis reduction to solve the problem. For a general multivariate modular linear equation with short solution in the given bounded range, the new method outputs this short solution in polynomial time, with a high probability. When the number of unknowns is not too large （smaller than 68）, the probability is approximating 1. Experimental results show that Knapsack systems and Lu-Lee type systems are easily broken in polynomial time with this new method.
