Quantum algorithms for some hidden shift problems

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2003, Pages 489-498

  Van Dam, Wim ^a   Hallgren, Sean ^b   Ip, Lawrence ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRYPTOGRAPHY; FOURIER TRANSFORMS; FUNCTIONS; POLYNOMIALS; QUANTUM THEORY; THEOREM PROVING;

HIDDEN COSET PROBLEM; LEGENDRE SYMBOL; PERIODICITY; QUANTUM ALGORITHMS;

ALGORITHMS;

EID: 0038754135     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (34)

1. Martin Abadi and Joan Feigenbaum. Secure circuit evaluation. A protocol based on hiding information from an oracle. Journal of Cryptology, 2(1):1-12, 1990.
2. Eric Bach and Jeffrey Shallit. Algorithmic Number Theory - Efficient Algorithms, volume I. MIT Press, Cambridge, USA, 1996.
3. Robert Beals. Quantum computation of Fourier transforms over symmetric groups. Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pages 48-53, 1997.
4. J. Niel de Beaudrap, Richard Cleve, and John Watrous. Sharp quantum vs. classical query complexity separations. quant-ph archive no. 0011065, 2001. Journal version to appear in Algorithmica.
5. Charles H. Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani. Strengths and weaknesses of quantum computing. SIAM Journal on Computing, 26(5):1510-1523, 1997.
6. Ethan Bernstein and Umesh Vazirani. Quantum complexity theory. SIAM Journal on Computing, 26(5):1411-1473, 1997.
7. Manuel Blum and Silvio Micali, How to generate cryptographically strong sequences of pseudo-random bits, SIAM Journal on Computing, 13(4):851-863, 1984.
8. Dan Boneh and Richard J. Lipton. Quantum crypt-analysis of hidden linear functions. Lecture Notes in Computer Science, 963:424-437, 1995.
9. Dan Boneh and Richard J. Lipton. Algorithms for black-box fields and their application to cryptography. Lecture Notes in Computer Science, 1109:283-297, 1996.
10. Richard Cleve, The query complexity of order-finding. Proceedings of the 15th Annual IEEE Conference on Computational Complexity, pages 54-59, 2000.
11. Richard Cleve and John Watrous. Fast parallel circuits for the quantum Fourier transform. Proceedings 41st Annual Symposium on Foundations of Computer Science, pages 526-536, 2000.
12. Wim van Dam. Quantum algorithms for weighing matrices and quadratic residues. quant-ph archive no. 0008059, 2000. Journal version to appear in Algorithmica.
13. Wim van Dam and Sean Hallgren. Efficient Quantum Algorithms for Shifted Quadratic Character Problems. quant-ph archive no. 0011067, 2000.
14. Wim van Dam and Gadiel Seroussi. Efficient Quantum Algorithms for Estimating Gauss Sums. quant-ph archive no. 0207131, 2002.
15. Ivan B. Damgård. On the randomness of Legendre and Jacobi sequences, Lecture Notes in Computer Science, 403:163-172, 1988.
16. Mark Ettinger and Peter Høyer. On Quantum Algorithms for Noncommutative Hidden Subgroups. quant-ph archive no. 9807029, 1998.
17. Mark Ettinger, Peter Høyer and Emanuel Knill. Hidden subgroup states are almost orthogonal. quant-ph archive no. 9901034, 1999.
18. Katalin Friedl, Frédéric Magniez, Miklos Santha and Pranab Sen. Quantum testers for hidden group properties quant-ph archive no. 0208184, 2002.
19. Michaelangelo Grigni, Leonard Schulman, Monica Vazirani and Umesh Vazirani. Quantum mechanical algorithms for the nonabelian hidden subgroup problem. Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, pages 68-74, 2001.
20. Lisa Hales. The quantum Fourier transform and extensions of the abelian hidden subgroup problem. Ph.D. Thesis, U.C. Berkeley, 2002.
21. Lisa Hales and Sean Hallgren. An improved quantum Fourier transform and appliations. Proceedings 41st Annual Symposium on Foundations of Computer Science, pages 515-525, 2000.
22. Sean Hallgren. Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem. Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, pages 653-658, 2001.
23. Sean Hallgren, Alexander Russell, and Amnon Ta-Shma. Normal subgroup reconstruction and quantum computation using group representations. Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, pages 627-635, 2000.
24. Lawrence Ip. Solving Shift Problems and the Hidden Coset Problem Using the Fourier Transform. quant-ph archive no. 0205034, 2002.
25. Gábor Ivanyos, Frédéric Magniez, and Miklos Santha. Efficient quantum algorithms for some instances of the non-abelian hidden subgroup problem. Proceedings of the Thirteenth Annual ACM Symposium on Parallel Algorithms and Architectures, pages 263-270, 2001.
26. Alexei Yu. Kitaev. Quantum measurements and the Abelian stabilizer problem. quant-ph archive no. 9511026, 1995.
27. Alexei Yu. Kitaev. Quantum computations: algorithms and error correction. Russian Mathematical Surveys, 52(6):1191-1249, 1997.
28. Rudolf Lidl and Harald Niederreiter. Finite Fields. volume 20 of Encyclopedia of Mathematics and Its Applications. Cambridge, second edition, 1997.
29. Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone. Handbook of Applied Cryptography. CRC Press, 1996.
30. Michelle Mosca and Arthur Ekert. The hidden subgroup problem and eigenvalue estimation on a quantum computer. Proceedings of the 1st NASA International Conference on Quantum Computing and Quantum Communication, Lecture Notes in Computer Science 1509, pages 174-188, 1999.
31. Peter W. Shor. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing, 26(5):1484-1509, 1997.
32. Daniel R. Simon. On the power of quantum computation. SIAM Journal on Computing, 26(5):1474-1483, 1997.
33. Richard Tolimieri, Miyoung An, and Chao Lu. Algorithms for Discrete Fourier Transform and Convolution. Springer-Verlag, 1989.
34. John Watrous. Quantum algorithms for solvable groups. Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, pages 60-67, 2001.