Quantum lower bound for the collision problem with small range

Theory of Computing

Volumn 1, Issue , 2005, Pages 29-36

  Kutin, Samuel ^a  

^a CENTER FOR COMMUNICATIONS RESEARCH   (United States)

Author keywords

Collision; Lower bound; Oracle; Polynomial method; Quantum; Query; Small range

Indexed keywords

COMPUTER PROGRAMMING;

COLLISION; LOWER BOUNDS; ORACLE; POLYNOMIAL METHODS; QUANTUM; QUERY; SMALL RANGE;

COMPUTER SCIENCE;

EID: 84921986319     PISSN: None     EISSN: 15572862     Source Type: Journal    
DOI: 10.4086/toc.2005.v001a002     Document Type: Article

References (11)

1. SCOTT AARONSON: Quantum lower bound for the collision problem. In Proc. of the 34th ACM STOC, pp. 635-642, 2002. [STOC:509907.509999, arXiv:quant-ph/0111102]. 1, 1, 2.1, 2
2. SCOTT AARONSON and YAOYUN SHI: Quantum lower bounds for the collision and the element distinctness problems. Journal of the ACM, 51(4):595-605, 2004. Based on [10] and [1]. [JACM:1008735]. 1, 1, 1
3. th IEEE FOCS, pp. 22-31, 2004. [FOCS:10.1109/FOCS.2004.54, arXiv:quant-ph/0311001]. 1, 1
4. ANDRIS AMBAINIS: Quantum lower bounds for collision and element distinctness with small range. Theory of Computing, 1(3), 2005. To appear. [ToC:v001/a003, arXiv:quant-ph/0305179]. 1, 1
5. BOB BEALS, HARRY BUHRMAN, RICHARD CLEVE, MICHELE MOSCA, and RONALD DEWOLF: Quantum lower bounds by polynomials. In Proc. of the 39th IEEE FOCS, pp. 352-361, 1998. [FOCS:10.1109/SFCS.1998.743485, arXiv:quant-ph/9802049]. 2.1, 2.1
6. GILLES BRASSARD, PETER HØYER, AND ALAIN TAPP: Quantum Cryptanalysis of Hash and Claw-Free Functions, volume 1380 of Lecture Notes in CS, pp. 163-169. Springer-Verlag, 1998. [LATIN:11bhjthw46dxl2qa, arXiv:quant-ph/9805082]. 1
7. LOV K. GROVER: A fast quantum mechanical algorithm for database search. In Proc. of the 28th ACM STOC, pp. 212-219, 1996. [STOC:237814.237866, arXiv:quant-ph/9605043]. 1
8. NOAM NISAN and MARIÓ SZEGEDY: On the degree of boolean functions as real polynomials. Computational Complexity, 4:301-313, 1994. [STOC:129757]. 1, 2.1
9. RAMAMOHAN PATURI: On the degree of polynomials that approximate symmetric Boolean functions. In Proc. of the 24th ACM STOC, pp. 468-474, 1992. [STOC:129758]. 1, 2.1
10. YAOYUN SHI: Quantum lower bounds for the collision and the element distinctness problems. In Proc. of the 43th IEEE FOCS, pp. 513-519, 2002. [FOCS:10.1109/SFCS.2002.1181975, arXiv:quant-ph/0112086]. 1, 1, 2.1, 2
11. 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. [SICOMP:29317].