**Books**

- , 2008,
*Encyclopedia of Algorithms*, Springer

**Journal Articles**

- Jintai Ding, Vlad Gheorghiu, Andras Gilyen, Sean Hallgren and Jianqiang Li, 2023, "Limitations of the Macaulay matrix approach for using the HHL algorithm to solve multivariate polynomial systems", Quantum,
**7**, pp. 1069

- Nai-Hui Chia, Sean Hallgren and Fang Song, 2020, "On Basing One-way Permutations on NP-hard Problems under Quantum Reductions", Quantum,
**4**, pp. 1-23

- Sean Hallgren, Adam D Smith and Fang Song, 2015, "Classical Cryptographic Protocols in a Quantum World", International Journal of Quantum Information,
**13**, (4)

- Kirsten Eisenträger, Sean Hallgren and Kristin E. Lauter, 2014, "Weak Instances of PLWE", IACR Cryptology ePrint Archive,
**2014**, pp. 784

- S. Hallgren, D. Nagaj and S. Narayanaswami, 2013, "The Local Hamiltonian Problem on a Line with Eight States is QMA-Complete", Quantum Information & Computation,
**13**, (9/10), pp. 721-750

- S. Hallgren, C. Moore, M. Rotteler, A. Russell and P. Sen, 2010, "Limitations of Quantum Coset States for Graph Isomorphism",
**57**, (6)

- Sean Hallgren, 2007, "Polynomial-time quantum algorithms for Pell’s equation and the principalideal problem", Journal of the ACM,
**54**, (1), pp. 1-19

- S. Hallgren, 2007, "The Local Hamiltonian Problem on a Line with Eight States is QMA-Complete",
**54**, (1), pp. 1-19

- Sean Hallgren, 2007, "Polynomial-time quantum algorithms for Pell’s equation and the principal
ideal problem", J. ACM,
**54**, (1)

- W. van Dam, Sean Hallgren and L. Ip, 2006, "Quantum Algorithms for Some Hidden Shift Problems",
**36**, (3), pp. 763-778

- S. Hallgren, A. Russell and A. Ta-Shma, 2003, "The Hidden Subgroup Problem and Quantum Computation Using Group Representations",
**32**, (4), pp. 916-934

- Wim van Dam and Sean Hallgren, 2000, "Efficient Quantum Algorithms for Shifted Quadratic Character Problems", CoRR,
**quant-ph/0011067**

**Conference Proceedings**

- Kirsten Eisentraeger, Sean Hallgren, Chris Leonardi, Travis Morrison and Jennifer Park, 2020, "Computing endomorphism rings of supersingular elliptic curves and connections to pathfinding in isogeny graphs",
**4**, (1), pp. 215-232

- Sean Hallgren, Eunou Lee and Ojas Parekh, 2020, "An Approximation Algorithm for the MAX-2-Local Hamiltonian Problem",
**176**, pp. 1-18

- Nai-Hui Chia and Sean Hallgren, 2016, "How Hard Is Deciding Trivial Versus Nontrivial in the Dihedral Coset Problem?", Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, Germany,
**61**, pp. 16

- Kirsten Eisenträger, Sean Hallgren and Kristin Lauter, 2014, "Weak instances of PLWE", pp. 12

- Kirsten Eisenträger, Sean Hallgren, Alexei Kitaev and Fang Song, 2014, "A quantum algorithm for computing the unit group of an arbitrary degree number field", pp. 293–302

- , 2014, "Selected Areas in Cryptography - SAC 2014 - 21st International Conference,
Montreal, QC, Canada, August 14-15, 2014, Revised Selected Papers", Springer,
**8781**

- , 2014, "Symposium on Theory of Computing, STOC 2014, New York, NY, USA,
May 31 - June 03, 2014", ACM

- S. Hallgren and K. Eisentraeger, 2012, "Computing the Unit Group, Class Group, and Compact Representations in Algebraic Function Fields", pp. 18

- Sean Hallgren, Adam D Smith and Fang Song, 2011, "Classical Cryptographic Protocols in a Quantum World", pp. 411–428

- , 2011, "Advances in Cryptology - CRYPTO 2011 - 31st Annual Cryptology Conference,
Santa Barbara, CA, USA, August 14-18, 2011. Proceedings", Springer,
**6841**

- Sean Hallgren, A. Smith and F. Song, 2011, "Classical Cryptographic Protocols in a Quantum World", Proceedings of the Fourteenth Workshop on Quantum Information Processing (QIP 2011), pp. 18

- Kirsten Eisenträger and Sean Hallgren, 2010, "Algorithms for Ray Class Groups and Hilbert Class Fields", pp. 471–483

- , 2010, "Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete
Algorithms, SODA 2010, Austin, Texas, USA, January 17-19, 2010", SIAM

- Sean Hallgren, Alexandra Kolla, Pranab Sen and Shengyu Zhang, 2008, "Making Classical Honest Verifier Zero Knowledge Protocols Secure againstQuantum Attacks", pp. 592–603

- Sean Hallgren and Aram Wettroth Harrow, 2008, "Superpolynomial Speedups Based on Almost Any Quantum Circuit", pp. 782–795

- , 2008, "Automata, Languages and Programming, 35th International Colloquium,
ICALP 2008, Reykjavik, Iceland, July 7-11, 2008, Proceedings, Part
I: Tack A: Algorithms, Automata, Complexity, and Games", Springer,
**5125**

- , 2008, "Automata, Languages and Programming, 35th International Colloquium,
ICALP 2008, Reykjavik, Iceland, July 7-11, 2008, Proceedings, Part
II - Track B: Logic, Semantics, and Theory of Programming &
Track C: Security and Cryptography Foundations", Springer,
**5126**

- Sean Hallgren, Alexandra Kolla, Pranab Sen and Shengyu Zhang, 2008, "Making Classical Honest Verifier Zero Knowledge Protocols Secure against
Quantum Attacks", pp. 592–603

- Sean Hallgren, Cristopher Moore, Martin Rötteler, Alexander Russell and Pranab Sen, 2006, "Limitations of quantum coset states for graph isomorphism", pp. 604–617

- , 2006, "Proceedings of the 38th Annual ACM Symposium on Theory of Computing,
Seattle, WA, USA, May 21-23, 2006", ACM

- Sean Hallgren, Alexander Russell and Igor Shparlinski, 2005, "Quantum Noisy Rational Function Reconstruction", pp. 420–429

- Sean Hallgren, 2005, "Fast quantum algorithms for computing the unit group and class groupof a number field", pp. 468–474

- , 2005, "Proceedings of the 37th Annual ACM Symposium on Theory of Computing,
Baltimore, MD, USA, May 22-24, 2005", ACM

- , 2005, "Computing and Combinatorics, 11th Annual International Conference,
COCOON 2005, Kunming, China, August 16-29, 2005, Proceedings", Springer,
**3595**

- Sean Hallgren, 2005, "Fast quantum algorithms for computing the unit group and class group
of a number field", pp. 468–474

- , 2003, "Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete
Algorithms, January 12-14, 2003, Baltimore, Maryland, USA", ACM/SIAM

- Wim van Dam, Sean Hallgren and Lawrence Ip, 2003, "Quantum algorithms for some hidden shift problems", pp. 489–498

- Sean Hallgren, 2002, "Polynomial-time quantum algorithms for Pell’s equation and the principalideal problem", pp. 653–658

- Sean Hallgren, 2002, "Polynomial-time quantum algorithms for Pell’s equation and the principal
ideal problem", pp. 653–658

- , 2002, "Proceedings on 34th Annual ACM Symposium on Theory of Computing,
May 19-21, 2002, Montréal, Québec, Canada", ACM

- Lisa Hales and Sean Hallgren, 2000, "An Improved Quantum Fourier Transform Algorithm and Applications", pp. 515–525

- Sean Hallgren, Alexander Russell and Amnon Ta-Shma, 2000, "Normal subgroup reconstruction and quantum computation using grouprepresentations", pp. 627–635

- , 2000, "41st Annual Symposium on Foundations of Computer Science, FOCS 2000,
12-14 November 2000, Redondo Beach, California, USA", IEEE Computer Society

- Sean Hallgren, Alexander Russell and Amnon Ta-Shma, 2000, "Normal subgroup reconstruction and quantum computation using group
representations", pp. 627–635

- , 2000, "Proceedings of the Thirty-Second Annual ACM Symposium on Theory
of Computing, May 21-23, 2000, Portland, OR, USA", ACM

- Lisa Hales and Sean Hallgren, 1999, "Quantum Fourier Sampling Simplified", pp. 330–338

- , 1999, "Proceedings of the Thirty-First Annual ACM Symposium on Theory of
Computing, May 1-4, 1999, Atlanta, Georgia, USA", ACM

- Kirsten Eisentraeger, Sean Hallgren, Kristin Lauter, Travis Morrison and Christophe Petit, , "Supersingular Isogeny Graphs and Endomorphism Rings: Reductions and Solutions"

**Abstracts**

- Sean Hallgren and Eunou Lee, , "An approximation algorithm for the MAX-2-Local Hamiltonian problem", 23th Annual Conference on Quantum Information Processing (QIP 2020)

**Other**

- Kirsten Eisentraeger, Sean Hallgren and Travis Morrison, 2017, "On the Hardness of Computing Endomorphism Rings of Supersingular Elliptic Curves", Cryptology ePrint Archive, Report 2017/986

- Nai-Hui Chia, Sean Hallgren and Fang Song, , "On basing one-way permutations on NP-hard problems under quantum reductions"