references.bib

@inproceedings{ajtai1996generating,
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}

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@inproceedings{ ajtaiKS01,
  author    = {Mikl{\'{o}}s Ajtai and
               Ravi Kumar and
               D. Sivakumar},
  editor    = {Jeffrey Scott Vitter and
               Paul G. Spirakis and
               Mihalis Yannakakis},
  title     = {A sieve algorithm for the shortest lattice vector problem},
  booktitle = {Proceedings on 33rd Annual {ACM} Symposium on Theory of Computing,
               July 6-8, 2001, Heraklion, Crete, Greece},
  pages     = {601--610},
  publisher = {{ACM}},
  year      = {2001} 
}

%

@book{alaca2004introductory,
  title={Introductory algebraic number theory},
  author={Alaca, {\c{S}}aban and Williams, Kenneth S},
  year={2004},
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}

%

@book{arora2009computational,
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  author={Arora, Sanjeev and Barak, Boaz},
  year={2009},
  publisher={Cambridge University Press}
}

%

@article{babai1986lovasz,
  title={On Lov{\'a}sz’lattice reduction and the nearest lattice point problem},
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}

%

@book{ bernstein09,
  title = {Post-Quantum Cryptography},
  author = {Daniel J. Bernstein and Johannes Buchmann and Erik Dahmen},
  publisher = {Springer},
  year = 2009
}

%

@inproceedings{brakerski2012fully,
  title={Fully homomorphic encryption without modulus switching from classical {GapSVP}},
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  booktitle={Annual Cryptology Conference},
  pages={868--886},
  year={2012},
  organization={Springer}
}

%

@article{brakerski2014efficient,
  title={Efficient fully homomorphic encryption from (standard) {LWE}},
  author={Brakerski, Zvika and Vaikuntanathan, Vinod},
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  volume={43},
  number={2},
  pages={831--871},
  year={2014},
  publisher={SIAM}
}

%

@article{brakerski2014leveled,
  title={({L}eveled) fully homomorphic encryption without bootstrapping},
  author={Brakerski, Zvika and Gentry, Craig and Vaikuntanathan, Vinod},
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}

%

@inproceedings{cai1997improved,
  title={An improved worst-case to average-case connection for lattice problems},
  author={Cai, Jin-Yi and Nerurkar, Ajay P},
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  organization={IEEE}
}

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@inproceedings{castryck2016provably,
  title={Provably weak instances of Ring-LWE revisited},
  author={Castryck, Wouter and Iliashenko, Ilia and Vercauteren, Frederik},
  booktitle={Annual International Conference on the Theory and Applications of Cryptographic Techniques},
  pages={147--167},
  year={2016},
  organization={Springer}
}

%

@article{chi15,
  author    = {Dong Pyo Chi and
               Jeong Woon Choi and
               Jeong San Kim and
               Taewan Kim},
  title     = {Lattice Based Cryptography for Beginners},
  journal   = {{IACR} Cryptol. ePrint Arch.},
  pages     = {938},
  year      = {2015},
}

%

@unpublished{conradcyclotomic,
  title={Cyclotomic extensions},
  series={Notes},
  author={Keith Conrad},
  year={2009},
  
}

%

@book{cormen01introduction,
  author = {Cormen, Thomas H. and Leiserson, Charles E. and Rivest, Ronald L. and Stein, Clifford},
  edition = {2nd},
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  title = {Introduction to Algorithms},
  year = 2001
}

%

@inproceedings{dijk2010fully,
  title={Fully homomorphic encryption over the integers},
  author={Dijk, Marten van and Gentry, Craig and Halevi, Shai and Vaikuntanathan, Vinod},
  booktitle={Annual international conference on the theory and applications of cryptographic techniques},
  pages={24--43},
  year={2010},
  organization={Springer}
}

%

@article{fan2012somewhat,
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  author={Fan, Junfeng and Vercauteren, Frederik},
  journal={IACR Cryptol. ePrint Arch.},
  volume={2012},
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  year={2012},
  publisher={Citeseer}
}


%

@inproceedings{gentry2009fully,
  title={Fully homomorphic encryption using ideal lattices},
  author={Gentry, Craig},
  booktitle={Proceedings of the 41st Annual ACM Symposium on Theory of Computing},
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  year={2009}
}

%

@article{gentry2010computing,
  title={Computing arbitrary functions of encrypted data},
  author={Gentry, Craig},
  journal={Communications of the ACM},
  volume={53},
  number={3},
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  year={2010},
  publisher={ACM New York, NY, USA}
}

%

@incollection{ halevi2017homomorphic,
  author = "Shai Halevi",
  title = "Homomorphic Encryption",
  booktitle = "Tutorials on the Foundations of Cryptography",
  editor = "Y. Lindell",
  publisher = "Springer",
  year = 2017
}

%

@book{hoffstein2008introduction,
  title={An introduction to mathematical cryptography},
  author={Hoffstein, Jeffrey and Pipher, Jill and Silverman, Joseph H},
  volume={1},
  year={2008},
  publisher={Springer}
}

%

@book{katz2014introduction,
  title={Introduction to modern cryptography},
  author={Katz, Jonathan and Lindell, Yehuda},
  year={2014},
  publisher={CRC press}
}

%

@incollection{ khot10,
  author    = {Subhash Khot},
  editor    = {Phong Q. Nguyen and
               Brigitte Vall{\'{e}}e},
  title     = {Inapproximability Results for Computational Problems on Lattices},
  booktitle = {The {LLL} Algorithm - Survey and Applications},
  series    = {Information Security and Cryptography},
  pages     = {453--473},
  publisher = {Springer},
  year      = {2010}
}

%

@article{ khot05,
  author    = {Subhash Khot},
  title     = {Hardness of approximating the shortest vector problem in lattices},
  journal   = {J. {ACM}},
  volume    = {52},
  number    = {5},
  pages     = {789--808},
  year      = {2005}
}

%

@article{korkine1873,
  title={Sur les formes quadratiques},
  author={A. Korkine and G. Zolotareff},
  journal={Mathematische Annalen},
  volume={6},
  pages={366-389},
  year={1873}
}

%

@inproceedings{lyubashevsky2010ideal,
  title={On ideal lattices and learning with errors over rings},
  author={Lyubashevsky, Vadim and Peikert, Chris and Regev, Oded},
  booktitle={Annual International Conference on the Theory and Applications of Cryptographic Techniques},
  pages={1--23},
  year={2010},
  organization={Springer}
}

%

@book{ micciancio-goldwasser02,
  author    = {Daniele Micciancio and
               Shafi Goldwasser},
  title     = {Complexity of lattice problems - a cryptograhic perspective},
  series    = {The Kluwer international series in engineering and computer science},
  volume    = {671},
  publisher = {Springer},
  year      = {2002}
}

%

@incollection{micciancio11lattice,
  author    = {Daniele Micciancio},
  editor    = {Henk C. A. van Tilborg and
               Sushil Jajodia},
  title     = {Lattice-Based Cryptography},
  booktitle = {Encyclopedia of Cryptography and Security, 2nd Ed},
  pages     = {713--715},
  publisher = {Springer},
  year      = {2011}
}

%

@article{micciancio07worst,
  author    = {Daniele Micciancio and
               Oded Regev},
  title     = {Worst-Case to Average-Case Reductions Based on Gaussian Measures},
  journal   = {{SIAM} J. Comput.},
  volume    = {37},
  number    = {1},
  pages     = {267--302},
  year      = {2007}
}

% 

@mastersthesis{mukherjee2016cyclotomic,
  title={Cyclotomic Polynomials in Ring-LWE Homomorphic Encryption Schemes},
  author={Mukherjee, Tamalika},
  school={Rochester Institute of Technology},
  year={2016}
}

%

@book{nguyen2010,
    title={The LLL algorithm},
    subtitle={Survey and Applications},
    author={Nguyen, Phong and Vallée, Brigitte},
    year={2010},
    publisher={Springer, Berlin, Heidelberg}
}

%

@inproceedings{peikert2007lattices,
  title={Lattices that admit logarithmic worst-case to average-case connection factors},
  author={Peikert, Chris and Rosen, Alon},
  booktitle={Proceedings of the 39th Annual ACM Symposium on Theory of Computing},
  pages={478--487},
  year={2007}
}

%

@inproceedings{peikert2009public,
  title={Public-key cryptosystems from the worst-case shortest vector problem},
  author={Peikert, Chris},
  booktitle={Proceedings of the 41st annual ACM symposium on Theory of computing},
  pages={333--342},
  year={2009}
}

%

@article{ peikert16decade,
  author    = {Chris Peikert},
  title     = {A Decade of Lattice Cryptography},
  journal   = {Found. Trends Theor. Comput. Sci.},
  volume    = {10},
  number    = {4},
  pages     = {283--424},
  year      = {2016}
}

%

@inproceedings{ pietrzak12,
  author    = {Krzysztof Pietrzak},
  editor    = {M{\'{a}}ria Bielikov{\'{a}} and
               Gerhard Friedrich and
               Georg Gottlob and
               Stefan Katzenbeisser and
               Gy{\"{o}}rgy Tur{\'{a}}n},
  title     = {Cryptography from Learning Parity with Noise},
  booktitle = {{SOFSEM} 2012: Theory and Practice of Computer Science - 38th Conference
               on Current Trends in Theory and Practice of Computer Science},
  series    = {Lecture Notes in Computer Science},
  volume    = {7147},
  pages     = {99--114},
  publisher = {Springer},
  year      = {2012}
}

%

@unpublished{ porter15cyclotomic,
  author = "Brett Porter",
  title = "Cyclotomic Polynomials",
  year = 2015
}

%

@article{reagen2020cheetah,
  title={Cheetah: Optimizations and Methods for Privacy Preserving Inference via Homomorphic Encryption},
  author={Reagen, Brandon and Choi, Wooseok and Ko, Yeongil and Lee, Vincent and Wei, Gu-Yeon and Lee, Hsien-Hsin S and Brooks, David},
  journal={arXiv preprint arXiv:2006.00505},
  year={2020}
}

%

@article{regev2009lattices,
  title={On lattices, learning with errors, random linear codes, and cryptography},
  author={Regev, Oded},
  journal={Journal of the ACM (JACM)},
  volume={56},
  number={6},
  pages={1--40},
  year={2009},
  publisher={ACM New York, NY, USA}
}

%

@article{regev2010learning,
  title={The learning with errors problem},
  author={Regev, Oded},
  journal={Invited survey in CCC},
  volume={7},
  number={30},
  pages={11},
  year={2010},
  publisher={Citeseer}
}

%

@inproceedings{regev05,
  author    = {Oded Regev},
  editor    = {Harold N. Gabow and
               Ronald Fagin},
  title     = {On lattices, learning with errors, random linear codes, and cryptography},
  booktitle = {Proceedings of the 37th Annual {ACM} Symposium on Theory of Computing},
  pages     = {84--93},
  publisher = {{ACM}},
  year      = {2005}
}

%

@article{rivest1978method,
  author = {Rivest, Ronald L. and Shamir, Adi and Adleman, Leonard M.},
  journal = {Commun. ACM},
  number = 2,
  pages = {120-126},
  title = {A Method for Obtaining Digital Signatures and Public-Key Cryptosystems.},
  volume = 21,
  year = 1978
}

%

@article{rivest1978data,
  author = {Rivest, R L and Adleman, L and Dertouzos, M L},
  journal = {Foundations of Secure Computation, Academic Press},
  pages = {169-179},
  title = {On Data Banks and Privacy Homomorphisms},
  year = 1978
}

%

@book{sipser2013introduction,
  author = {Sipser, Michael},
  edition = {Third},
  publisher = {Course Technology},
  title = {Introduction to the Theory of Computation},
  year = 2013
}


@article{sipser1996introduction,
  title={Introduction to the Theory of Computation},
  author={Sipser, Michael},
  journal={ACM Sigact News},
  volume={27},
  number={1},
  pages={27--29},
  year={1996},
  publisher={ACM New York, NY, USA}
}

%

@article{stein2012algebraic,
  title={Algebraic number theory, a computational approach},
  author={Stein, William},
  journal={Harvard, Massachusetts},
  year={2012}
}