New lattice based cryptographic constructions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
New lattice-based cryptographic constructions
Journal of the ACM (JACM)
The hidden subgroup problem and permutation group theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
The Symmetric Group Defies Strong Fourier Sampling
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On the impossibility of a quantum sieve algorithm for graph isomorphism
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum algorithms for Simon's problem over general groups
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum algorithm for a generalized hidden shift problem
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum algorithms for Simon's problem over nonabelian groups
ACM Transactions on Algorithms (TALG)
Recent progress in quantum algorithms
Communications of the ACM
Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
On the Impossibility of a Quantum Sieve Algorithm for Graph Isomorphism
SIAM Journal on Computing
For distinguishing conjugate hidden subgroups, the pretty good measurement is as good as it gets
Quantum Information & Computation
How a Clebsch-Gordan transform helps to solve the Heisenberg hidden subgroup problem
Quantum Information & Computation
Efficient quantum algorithm for identifying hidden polynomials
Quantum Information & Computation
On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems
Quantum Information & Computation
Computational indistinguishability between quantum states and its cryptographic application
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Random oracles in a quantum world
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
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We present the first explicit connection between quantum computation and lattice problems. Namely, we show a solution to the Unique Shortest Vector Problem (SVP) under the assumption that there exists an algorithm that solves the hidden subgroup problem on the dihedral group by coset sampling. Moreover, we solve the hidden subgroup problem on the dihedral group by using an average case subset sum routine. By combining the two results, we get a quantum reduction from \widetilde\Theta (n^{2.5} )-unique-SVP to the average case subset sum problem. This is a better connection than the known classical results.