Quantum Computation and Lattice Problems

Quantum Computation and Lattice Problems (2002)

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by Oded Regev

Venue:	Proc. 43rd Symposium on Foundations of Computer Science
Citations:	45 - 4 self

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@INPROCEEDINGS{Regev02quantumcomputation,
    author = {Oded Regev},
    title = {Quantum Computation and Lattice Problems},
    booktitle = {Proc. 43rd Symposium on Foundations of Computer Science},
    year = {2002},
    pages = {520--529}
}

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Abstract

We present the first explicit connection between quantum computation and lattice problems. Namely, we show a solution to the unique-SVP under the assumption that there exists...

Citations

1121	Quantum Computation and Quantum Information - Nielsen, Chuang - 2000
756	Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer - Shor - 1997
734	A fast quantum mechanical algorithm for database search - Grover - 1996
553	Factoring Polynomials with Rational Coefficients - Lenstra, Lovàsz - 1982
337	On the power of quantum computation - Simon - 1994
312	Rapid solutions of problems by quantum computation - Deutsch, Jozsa - 1992
163	A Public-Key Cryptosystem with Worst-Case/Average-Case Equivalence - Ajtai, Dwork - 1997
137	Quantum measurements and the Abelian Stabilizer Problem lanl e-print quant-ph/9511026 - Kitaev
124	Generating hard instances of lattice problems - Ajtai - 2004
82	Factoring polynomials with rational coe cients - Lenstra, Lenstra, et al. - 2001
82	Complexity of Lattice Problems: A Cryptographic Perspective - Micciancio, Goldwasser - 2002
69	Efficient cryptographic schemes provably as secure as subset sum - Impagliazzo, Naor - 1996
66	On quantum algorithms for noncommutative hidden subgroups - Ettinger, Høyer - 1998
65	Polynomial-Time Quantum Algorithms for Pell’s Equation and the Principal Ideal Problem - Hallgren - 2002
62	Quantum mechanical algorithms for the nonabelian hidden subgroup problem - Grigni, Schulman, et al.
52	Random walks and an O ∗ (n 5 ) volume algorithm for convex bodies. Random Struct. Algorithms - Kannan, Lovász, et al. - 1997
50	An improved worst-case to average-case connection for lattice problems (extended abstract - Cai, Nerurkar - 1997
44	A subexponential-time quantum algorithm for the dihedral hidden subgroup problem - Kuperberg
40	Polynomial-time solution to the hidden subgroup problem for a class of non-abelian groups - Roetteler, Beth - 1998
37	New lattice based cryptographic constructions - Regev - 2003
34	Normal subgroup reconstruction and quantum computing using group representations - Hallgren, A, et al. - 2000
30	Hidden translation and orbit coset in quantum computing - Friedl, Ivanyos, et al. - 2003
29	Random walks and an O (n ) volume algorithm for convex bodies, Random Structures & Algorithms - Kannan, Lov'asz, et al.
13	Creating superpositions that correspond to efficiently integrable probability distributions - Grover, Rudolph
9	Improved cryptographic hash functions with worst-case/average-case connection - Micciancio - 2002
8	Approximation of diameters: randomization doesn’t help - Brieden, Gritzmann, et al. - 1998
6	Algorithms for hidden coset problems - Dam, Hallgren, et al. - 2003
3	A new transference theorem and applications to Ajtai’s connection factor - Cai - 1998
3	The graph isomorphism problem: its structural complexity - Johannes, Uwe, et al. - 1993