Explicit Hard Instances of the Shortest Vector Problem
PQCrypto '08 Proceedings of the 2nd International Workshop on Post-Quantum Cryptography
An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups
Mathematical Methods in Computer Science
Quantum algorithms using the curvelet transform
Proceedings of the forty-first annual ACM symposium on Theory of computing
On the complexity of the hidden subgroup problem
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
An efficient quantum algorithm for the hidden subgroup problem in nil-2 groups
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Limitations of quantum coset states for graph isomorphism
Journal of the ACM (JACM)
Complexity classes of equivalence problems revisited
Information and Computation
Quantum measurements for hidden subgroup problems with optimal sample complexity
Quantum Information & Computation
Efficient quantum algorithms for the hidden subgroup problem over semi-direct product groups
Quantum Information & Computation
On solving systems of random linear disequations
Quantum Information & Computation
Quantum algorithm for the Boolean hidden shift problem
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Solutions to the hidden subgroup problem on some metacyclic groups
TQC'09 Proceedings of the 4th international conference on Theory of Quantum Computation, Communication, and Cryptography
Finding hidden Borel subgroups of the general linear group
Quantum Information & Computation
Quipper: a scalable quantum programming language
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
Classical hardness of learning with errors
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
An introduction to quantum programming in quipper
RC'13 Proceedings of the 5th international conference on Reversible Computation
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We present the first explicit connection between quantum computation and lattice problems. Namely, our main result is 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. Additionally, we present an approach to solving the hidden sub-group problem on the dihedral group by using an average case subset sum routine.