Quantum Computational Number Theory
暂无分享,去创建一个
[1] Silvio Micali,et al. The knowledge complexity of interactive proof-systems , 1985, STOC '85.
[2] Dan Boneh,et al. TWENTY YEARS OF ATTACKS ON THE RSA CRYPTOSYSTEM , 1999 .
[3] J. McKee. Turning Euler's Factoring Method into a Factoring Algorithm , 1996 .
[4] Umesh V. Vazirani,et al. Quantum Complexity Theory , 1997, SIAM J. Comput..
[5] José Manuel,et al. Controlling the order of wedge filling transitions: the role of line tension , 2007 .
[6] R. Jozsa,et al. Quantum Computation and Shor's Factoring Algorithm , 1996 .
[7] Dieter Suter,et al. Quantum adiabatic algorithm for factorization and its experimental implementation. , 2008, Physical review letters.
[8] Jian-Wei Pan,et al. Demonstration of a compiled version of Shor's quantum factoring algorithm using photonic qubits. , 2007, Physical review letters.
[9] Martin Gennis,et al. Explorations in Quantum Computing , 2001, Künstliche Intell..
[10] J. Groβchadl. The Chinese Remainder Theorem and its application in a high-speed RSA crypto chip , 2000 .
[11] X-Q Zhou,et al. Experimental realization of Shor's quantum factoring algorithm using qubit recycling , 2011, Nature Photonics.
[12] Christof Zalka. Fast versions of Shor's quantum factoring algorithm , 1998 .
[13] Anthony J. G. Hey,et al. Feynman Lectures on Computation , 1996 .
[14] H. Riesel. Prime numbers and computer methods for factorization , 1985 .
[15] Shirley Dex,et al. JR 旅客販売総合システム(マルス)における運用及び管理について , 1991 .
[16] Andrew M. Childs,et al. Quantum algorithms for algebraic problems , 2008, 0812.0380.
[17] P. L. Montgomery,et al. A survey of modern integer factorization algorithms , 1994 .
[18] D. Deutsch. Quantum computational networks , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.
[19] Colin P. Williams. Explorations in Quantum Computing, Second Edition , 2011, Texts in Computer Science.
[20] M. Hinek. Cryptanalysis of RSA and Its Variants , 2009 .
[21] P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .
[22] N. Mermin. Quantum Computer Science: An Introduction , 2007 .
[23] David P. DiVincenzo,et al. Quantum information and computation , 2000, Nature.
[24] Griffiths,et al. Semiclassical Fourier transform for quantum computation. , 1995, Physical review letters.
[26] I. Chuang,et al. Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance , 2001, Nature.
[27] Graeme Smith,et al. Oversimplifying quantum factoring , 2013, Nature.
[28] D. Shanks. Class number, a theory of factorization, and genera , 1971 .
[29] Don Coppersmith,et al. Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities , 1997, Journal of Cryptology.
[30] J. M. Pollard,et al. Theorems on factorization and primality testing , 1974, Mathematical Proceedings of the Cambridge Philosophical Society.
[31] Richard P. Brent,et al. An improved Monte Carlo factorization algorithm , 1980 .
[32] R. Feynman. Simulating physics with computers , 1999 .
[33] Michael J. Wiener,et al. Cryptanalysis of Short RSA Secret Exponents (Abstract) , 1990, EUROCRYPT.
[34] J. Dixon. Factorization and Primality Tests , 1984 .
[35] Nikesh S. Dattani,et al. Quantum factorization of 56153 with only 4 qubits , 2014, ArXiv.
[36] James McKee,et al. Old and New Deterministic Factoring Algorithms , 1996, ANTS.
[37] J. Brillhart,et al. A method of factoring and the factorization of , 1975 .
[38] B. Lanyon,et al. Experimental demonstration of a compiled version of Shor's algorithm with quantum entanglement. , 2007, Physical review letters.
[39] Daniel R. Simon,et al. On the power of quantum computation , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.
[40] Peter W. Shor,et al. Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..
[41] Carl Pomerance,et al. A Tale of Two Sieves , 1998 .
[42] Gilles Brassard,et al. Strengths and Weaknesses of Quantum Computing , 1997, SIAM J. Comput..
[43] Oded Goldreich,et al. Foundations of Cryptography: Basic Tools , 2000 .
[44] Song Y. Yan. Primality Testing and Integer Factorization in Public-Key Cryptography , 2009, Advances in Information Security.
[45] Carl Pomerance,et al. The Quadratic Sieve Factoring Algorithm , 1985, EUROCRYPT.
[46] Minyi Guo,et al. Molecular solutions of the RSA public-key cryptosystem on a DNA-based computer , 2012, The Journal of Supercomputing.
[47] Jean-Pierre Seifert,et al. Using Fewer Qubits in Shor's Factorization Algorithm Via Simultaneous Diophantine Approximation , 2001, CT-RSA.
[48] D. Browne. Efficient classical simulation of the quantum Fourier transform , 2006, quant-ph/0612021.
[49] John Watrous,et al. Quantum Computational Complexity , 2008, Encyclopedia of Complexity and Systems Science.
[50] Adi Shamir,et al. A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.
[51] Peggy Aycinena. Access for all , 2008, CACM.
[52] Peter W. Shor,et al. Algorithms for quantum computation: discrete logarithms and factoring , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.
[53] J. Pollard. A monte carlo method for factorization , 1975 .
[54] Raymond Laflamme,et al. Quantum Computers, Factoring, and Decoherence , 1995, Science.
[55] Andrew Chi-Chih Yao,et al. Quantum Circuit Complexity , 1993, FOCS.
[56] Leonard M. Adleman,et al. Quantum Computability , 1997, SIAM J. Comput..
[57] M. Rabin. DIGITALIZED SIGNATURES AND PUBLIC-KEY FUNCTIONS AS INTRACTABLE AS FACTORIZATION , 1979 .
[58] Michael R. Geller,et al. Factoring 51 and 85 with 8 qubits , 2013, Scientific Reports.
[59] Jean-Sébastien Coron,et al. Deterministic Polynomial-Time Equivalence of Computing the RSA Secret Key and Factoring , 2006, Journal of Cryptology.
[60] H. W. Lenstra,et al. Factoring integers with elliptic curves , 1987 .
[61] Igor L. Markov,et al. Faster Quantum Number Factoring via Circuit Synthesis , 2013, ArXiv.
[62] Jiangfeng Du,et al. Quantum factorization of 143 on a dipolar-coupling nuclear magnetic resonance system. , 2012, Physical review letters.
[63] P. Shor. INTRODUCTION TO QUANTUM ALGORITHMS , 2000, quant-ph/0005003.
[64] D. Deutsch. Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.
[65] John Watrous,et al. Guest column: an introduction to quantum information and quantum circuits 1 , 2011, SIGA.
[66] Stefan Katzenbeisser,et al. Recent Advances in RSA Cryptography , 2001, Advances in Information Security.
[67] N. Mermin. Quantum Computer Science , 2007 .
[68] Weng-Long Chang,et al. Fast parallel molecular algorithms for DNA-based computation: factoring integers , 2005, IEEE Transactions on NanoBioscience.
[69] W. Schleich,et al. Factorization of numbers with the temporal Talbot effect: optical implementation by a sequence of shaped ultrashort pulses. , 2007, Physical review letters.
[70] Isaac L. Chuang,et al. Quantum Computation and Quantum Information (10th Anniversary edition) , 2011 .
[71] Jr.,et al. Shor's Quantum Factoring Algorithm , 2000, quant-ph/0010034.
[72] Peter W. Shor,et al. Why haven't more quantum algorithms been found? , 2003, JACM.
[73] Rodney Van Meter,et al. Architecture of a Quantum Multicomputer Implementing Shor's Algorithm , 2008, TQC.
[74] Wade Trappe,et al. Introduction to Cryptography with Coding Theory , 2002 .
[75] Christof Zalka,et al. Shor's discrete logarithm quantum algorithm for elliptic curves , 2003, Quantum Inf. Comput..
[76] P. K. Aravind,et al. A pseudo-simulation of Shor's quantum factoring algorithm , 2002 .
[77] R. Mollin. RSA and Public-Key Cryptography , 2002 .
[78] Martin E. Hellman,et al. An improved algorithm for computing logarithms over GF(p) and its cryptographic significance (Corresp.) , 1978, IEEE Trans. Inf. Theory.
[79] M. Pohst. Computational Algebraic Number Theory , 1993 .
[80] R. V. Meter,et al. Fast quantum modular exponentiation , 2004, quant-ph/0408006.
[81] Dave Bacon,et al. Recent progress in quantum algorithms , 2010, Commun. ACM.
[82] G. G. Stokes. "J." , 1890, The New Yale Book of Quotations.
[83] E. Lucero,et al. Computing prime factors with a Josephson phase qubit quantum processor , 2012, Nature Physics.
[84] Leonard M. Adleman,et al. Algorithmic number theory-the complexity contribution , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.
[85] Mike Gardner. A new kind of cipher that would take millions of years to break , 1997 .
[86] Ron Knott,et al. Prime numbers - a computational perspective (2nd edn), by Richard Crandall and Carl Pomerance. Pp. 597. £42.50 (hbk). 2005. ISBN 0-387-25282-7 (Springer Verlag). , 2008, The Mathematical Gazette.
[87] R. K. Shyamasundar,et al. Introduction to algorithms , 1996 .
[88] Colin P. Williams,et al. Ultimate zero and one - computing at the quantum frontier , 2012 .