XIA Pei-su. Quantum computing[J]. Journal of Computer Research and Development, 2001, 38(10): 1153-1171. (in Chinese)
[3]
FEYNMAN R P. Simulating physics with computers[J]. International Journal of Theoretical Physics, 1982, 21(6/7): 467-488.
[4]
DEUTSCH D. Quantum theory, the Church-Turing principle and the universal quantum computer[J]. Proceedings of the Royal Society London, 1985, A400: 97-117.
[5]
SHOR P W. Polynomial-time algorithms for prime factorizati-on and discrete logarithms on a quantum computer[J]. SIAM Journal on Computing, 1997, 26(5): 1484-1509.
[6]
GROVER L K. A fast quantum mechanical algorithm for database search[C]//Proceeding of 28th ACM Symposium on Theory of Computation(STOC'96). New York: ACM, 1996: 212-219.
Lü Xin, FENG Deng-guo. Quantum algorithm analysis of knapsack problem [J]. Journal of Beijing University of Aeronautics and Astronautics, 2004, 30 (11): 1088-1091. (in Chinese)
[9]
WANG Hong-fu, ZHANG Shou, ZHAO Yong-fang, et al. Quantum mechanical algorithm for solving quadratic residue equation[J]. International Journal of Theoretical Physics, 2009, 48: 3262-3267.
[10]
RABIN M. Digitalized sigratures and public-key encryptions as intractable as factorization[R]. MA: MIT, 1979.
[11]
PASCAL P, DAVID P. Efficientpublic-pey cryptosystems provably secure against active adversaries[C]//Advances in Cryptology-ASIACRYPT'99. London: Springer-Verlag, 1999.
[12]
SU Sheng-hui, Lü Shu-wang. To solve the high degree congruence xn≡a (mod p) in GF(p)[C]//Proc of Int Conference on Computation Intelligence and Security. New Jersey: IEEE, 2007: 672-676.
[13]
YAN Song-yuan. Number theory for computing [M]. Berlin: Springer-Verlag, 2002: 225-228.
[14]
NIELSEN M A, CHUANG I L. Quantum computation and quantum information [M]. Cambridge: Cambridge University Press, 2000: 171-202.
[15]
GORDON D M. Discrete logarithms in GF(p) using the number field sieve[J]. Society for Industrial and Applied Mathematics Journal on Discrete Mathematics, 1993, 6(1): 124-138.
[16]
潘承洞, 潘承彪. 初等数论[M]. 2 版. 北京: 北京大学出版社, 2003: 16-21.
[17]
BRASSARD G, HOYER P, TAPP A. Quantum counting[C] //Proceedings of 25th International Colloquium Automata Language and Programming ( ICALP'98 ). Berlin: Springer-Verlag, 1998, 1443: 820-831.
[18]
BENNETT C H. Time/ space trade-offs for reversible computaion[J]. SIAM J Comput, 1989, 18: 766-776.
[19]
SCHONHAGE A, STRASSEN V. Schnelle multiplication grosser zahlen[J]. Computing, 1971, 7 (3/4): 281-292.
FU Xiang-qun, BAO Wan-su, ZHOU Chun, et al. Quantum algorithm for prime factorization with high probability[J]. Acta Electronica Sinica, 2011, 39(1): 36-39. (in Chinese)
