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学者姓名：徐茂智
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摘要 ：
求根问题是计算数论中的一个困难性问题,为了提高求根问题的求解效率和扩大量子计算的应用范围,对求根问题进行了量子算法的分析.在两大量子算法Shor算法和Grover算法的基础上,提出了2种解决求根问题的量子算法RF-Shor算法和RF-Grover算法.经分析,RF-Shor算法需要多项式规模的量子门资源,能以接近1的概率求出求根问题的所有解.在没有使用任何可提高搜索效率的经典策略的情况下,RF-Grover算法能在O(M/k)步内以至少1/2的概率求出求根问题k个解中的一个解.
关键词 ：
Shor算法 Shor算法 求根问题 求根问题 量子算法 量子算法 Grover算法 Grover算法
引用：
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| GB/T 7714 | 孙国栋 , 苏盛辉 , 徐茂智 . 求根问题的量子计算算法 [J]. | 北京工业大学学报 , 2015 , 41 (03) : 366-371 . |
| MLA | 孙国栋 等. "求根问题的量子计算算法" . | 北京工业大学学报 41 . 03 (2015) : 366-371 . |
| APA | 孙国栋 , 苏盛辉 , 徐茂智 . 求根问题的量子计算算法 . | 北京工业大学学报 , 2015 , 41 (03) , 366-371 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Root finding problem is a hard problem in computational number theory. To improve the efficiency of solving the problem and expand the scope of applications of quantum computing, the quantum algorithms for solving the root finding problem are analyzed in this paper. Based on the two important quantum algorithms-Shor's algorithm and Grover's algorithm, two quantum mechanical algorithms are proposed to solve the root finding problem, which are named RF-Shor algorithm and RF-Grover algorithm. According to the analysis, the RF-Shor algorithm can find all the solutions to the root finding problem with a probability closed to 100%, with a consumption of polynomial quantum gates; the RF-Grover algorithm does not involve any classical method to improve the search efficiency and one of the k solutions to the root finding problem can be obtained in O(√M/k)1/2) steps with a probability of at least 50%. ©, 2015, Beijing University of Technology. All right reserved.
关键词 ：
Grover's algorithm; Quantum mechanical algorithms; Root finding problem; Shor's algorithm Grover's algorithm; Quantum mechanical algorithms; Root finding problem; Shor's algorithm
引用：
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| GB/T 7714 | Sun, G.-D. , Su, S.-H. , Xu, M.-Z. . Quantum mechanical algorithms for solving root finding problem [J]. | Journal of Beijing University of Technology , 2015 , 41 (3) : 366-371 . |
| MLA | Sun, G.-D. 等. "Quantum mechanical algorithms for solving root finding problem" . | Journal of Beijing University of Technology 41 . 3 (2015) : 366-371 . |
| APA | Sun, G.-D. , Su, S.-H. , Xu, M.-Z. . Quantum mechanical algorithms for solving root finding problem . | Journal of Beijing University of Technology , 2015 , 41 (3) , 366-371 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
The authors give the definition and property of a bit-pair shadow, and design the algorithms of a public key cryptoscheme based on a multivariate permutation problem and an anomalous subset product problem to which no subexponential time solutions are found so far, and regards a bit-pair as an operation unit. Further, demonstrate that the decryption algorithm is correct, deduce the probability that a plaintext solution is nonunique is nearly zero, analyze the security of the new scheme against extracting a private key from a public key and recovering a plaintext from a ciphertext on the assumption that an integer factorization problem, a discrete logarithm problem, and a low-density subset sum problem can be solved efficiently, and prove that new scheme using random padding and permutation is semantically secure. The analysis shows that the bit-pair method increases the density D of a related knapsack to 1+, and decreases the modulus length inverted right perpendicular lg M inverted left perpendicular of the new scheme to 464, 544, or 640.
关键词 ：
Anomalous subset sum problem Anomalous subset sum problem Bit-pair shadow Bit-pair shadow Compact sequence Compact sequence Public key cryptoscheme Public key cryptoscheme Random padding Random padding Semantical security Semantical security
引用：
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| GB/T 7714 | Su, Shenghui , Lu, Shuwang , Xu, Maozhi . A Public Key Cryptoscheme Using Bit-Pairs with Provable Semantical Security [C] . 2015 : 674-686 . |
| MLA | Su, Shenghui 等. "A Public Key Cryptoscheme Using Bit-Pairs with Provable Semantical Security" . (2015) : 674-686 . |
| APA | Su, Shenghui , Lu, Shuwang , Xu, Maozhi . A Public Key Cryptoscheme Using Bit-Pairs with Provable Semantical Security . (2015) : 674-686 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
针对确定性公钥密码体制不能抵抗选择明文攻击的弱点,基于REESSE1+公钥密码体制设计2种概率加密方案,使同一明文对应的密文具有不确定性。方案1在明文比特序列的奇数位置插入相同长度的随机比特串,产生新的随机明文序列,并对该序列进行加密;方案2对公钥序列进行重新排列,使用新的公钥序列对明文进行加密。证明2种方案的正确性,并对其安全性和性能进行分析,结果表明,2种方案均可抵抗选择明文攻击,密码强度至少等价于基于离散对数问题的密码方案,同时,其加解密运行时间均少于基于RSA和剩余问题的概率密码方案。
关键词 ：
概率加密 概率加密 多变量组合问题 多变量组合问题 选择明文攻击 选择明文攻击 非范子集积问题 非范子集积问题 互素序列 互素序列 REESSE1+公钥密码体制 REESSE1+公钥密码体制
引用：
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| GB/T 7714 | 孙国栋 , 苏盛辉 , 徐茂智 . 基于REESSE1+公钥密码体制的概率加密 [J]. | 计算机工程 , 2014 , 40 (12) : 78-82 . |
| MLA | 孙国栋 等. "基于REESSE1+公钥密码体制的概率加密" . | 计算机工程 40 . 12 (2014) : 78-82 . |
| APA | 孙国栋 , 苏盛辉 , 徐茂智 . 基于REESSE1+公钥密码体制的概率加密 . | 计算机工程 , 2014 , 40 (12) , 78-82 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Quantum computation is a new computing model based on fundamental quantum mechanical principle. Grover's algorithm finds the solution for a searching problem in the square root time of exhaustive search. Brassard, Hoyer, Tapp's algorithm counts the number of solutions for a searching problem. Through exploiting the two quantum algorithms, we propose a quantum algorithm for solving a new cryptography problem----polynomial root finding problem, which could be used to design a cryptosystem. The algorithm will take O(root M/t) steps for finding one of the t solutions to the problem, where M is the modular of the equation. The success rate of the algorithm is a constant and the cost of the algorithm depends on the calculations of modular exponentiation and the number of iterations.
关键词 ：
Polynomial root finding problem Polynomial root finding problem Quantum counting Quantum counting Quantum searching Quantum searching Signature algorithm Signature algorithm
引用：
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| GB/T 7714 | Sun, Guodong , Su, Shenghui , Xu, Maozhi . Quantum Algorithm for Polynomial Root Finding Problem [C] . 2014 : 469-473 . |
| MLA | Sun, Guodong 等. "Quantum Algorithm for Polynomial Root Finding Problem" . (2014) : 469-473 . |
| APA | Sun, Guodong , Su, Shenghui , Xu, Maozhi . Quantum Algorithm for Polynomial Root Finding Problem . (2014) : 469-473 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Quantum computation is a new computational model based on quantum mechanical principle. Shor invented the polynomial time algorithms for the prime factorization and discrete logarithm problem, which indicated that the cryptosystems based on them are totally unsafe in the quantum world. Grover constructed an algorithm that finds a solution in only O(√2 n )steps whereas the exhaustive search algorithm needs O(2 n ) steps on average. In this paper we investigate the cryptanalysis of a new cryptography problem-multivariate permutation problem (MPP), which could be used to design public-key cryptosystem, with the help of the two quantum algorithms. Specially, we discuss the strength of a private key of the REESSE1+ public-key cryptosystem, whose security is based on the hardness of MPP. Besides, some suggestions are also given about the implementation of the REESSE1+.
关键词 ：
Algorithms Algorithms Factorization Factorization Polynomial approximation Polynomial approximation Public key cryptography Public key cryptography Quantum computers Quantum computers Quantum cryptography Quantum cryptography Quantum theory Quantum theory
引用：
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| GB/T 7714 | Sun, Guodong , Su, Shenghui , Xu, Maozhi . Quantum cryptanalysis of multivariate permutation problem [J]. | International Journal of Security and its Applications , 2014 , 8 (6) : 261-272 . |
| MLA | Sun, Guodong 等. "Quantum cryptanalysis of multivariate permutation problem" . | International Journal of Security and its Applications 8 . 6 (2014) : 261-272 . |
| APA | Sun, Guodong , Su, Shenghui , Xu, Maozhi . Quantum cryptanalysis of multivariate permutation problem . | International Journal of Security and its Applications , 2014 , 8 (6) , 261-272 . |
| 导入链接 | NoteExpress RIS BibTex |
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