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Discrete weighted transforms and large-integer arithmetic

Authors:

Richard Crandall,

Barry FaginAuthors Info & Claims

Mathematics of Computation, Volume 62, Issue 205

Pages 305 - 324

https://doi.org/10.2307/2153411

Published: 01 January 1994 Publication History

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Jonatan GCho HSon HWu XLivesay NMora EShivdikar KAbellán JJoshi AKaeli DKim J(2024)Scalability Limitations of Processing-in-Memory using Real System EvaluationsProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/36390468:1(1-28)Online publication date: 21-Feb-2024
https://dl.acm.org/doi/10.1145/3639046
Sabbagh Molahosseini AVandierendonck HQuek TGao DZhou JCardenas A(2024)Exploiting Data Redundancy in CKKS Encoding for High-Speed Homomorphic EncryptionProceedings of the 19th ACM Asia Conference on Computer and Communications Security10.1145/3634737.3656292(990-1002)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1145/3634737.3656292
Yang HShen SDai WZhou LLiu ZZhao Y(2024)Phantom: A CUDA-Accelerated Word-Wise Homomorphic Encryption LibraryIEEE Transactions on Dependable and Secure Computing10.1109/TDSC.2024.336390021:5(4895-4906)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1109/TDSC.2024.3363900
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Index Terms

Discrete weighted transforms and large-integer arithmetic
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Computation of transforms
      2. Number-theoretic computations

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Mathematics of Computation Volume 62, Issue 205

Jan. 1994

419 pages

ISSN:0025-5718

Editor:
Walter Gautschi
Providence, RI

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American Mathematical Society

United States

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Published: 01 January 1994

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Jonatan GCho HSon HWu XLivesay NMora EShivdikar KAbellán JJoshi AKaeli DKim J(2024)Scalability Limitations of Processing-in-Memory using Real System EvaluationsProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/36390468:1(1-28)Online publication date: 21-Feb-2024
https://dl.acm.org/doi/10.1145/3639046
Sabbagh Molahosseini AVandierendonck HQuek TGao DZhou JCardenas A(2024)Exploiting Data Redundancy in CKKS Encoding for High-Speed Homomorphic EncryptionProceedings of the 19th ACM Asia Conference on Computer and Communications Security10.1145/3634737.3656292(990-1002)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1145/3634737.3656292
Yang HShen SDai WZhou LLiu ZZhao Y(2024)Phantom: A CUDA-Accelerated Word-Wise Homomorphic Encryption LibraryIEEE Transactions on Dependable and Secure Computing10.1109/TDSC.2024.336390021:5(4895-4906)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1109/TDSC.2024.3363900
Chusov A(2022)Outperforming Sequential Full-Word Long Addition With Parallelization and VectorizationIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2022.321193733:12(4974-4985)Online publication date: 1-Dec-2022
https://dl.acm.org/doi/10.1109/TPDS.2022.3211937
Joye M(2021)Balanced Non-adjacent FormsAdvances in Cryptology – ASIACRYPT 202110.1007/978-3-030-92078-4_19(553-576)Online publication date: 6-Dec-2021
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Dai WChen DCheung RKoç Ç(2018)FFT-Based McLaughlin's Montgomery Exponentiation without Conditional SelectionsIEEE Transactions on Computers10.1109/TC.2018.281146667:9(1301-1314)Online publication date: 1-Sep-2018
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(2017)Sieving for shortest vectors in ideal latticesInternational Journal of Applied Cryptography10.1504/IJACT.2017.0893533:4(313-329)Online publication date: 1-Jan-2017
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Liu ZPöppelmann TOder TSeo HRoy SGüneysu TGroßschädl JKim HVerbauwhede I(2017)High-Performance Ideal Lattice-Based Cryptography on 8-Bit AVR MicrocontrollersACM Transactions on Embedded Computing Systems10.1145/309295116:4(1-24)Online publication date: 13-Jul-2017
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Larrieu RYap CEl Din M(2017)The Truncated Fourier Transform for Mixed RadicesProceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3087604.3087636(261-268)Online publication date: 23-Jul-2017
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Harvey Dvan der Hoeven JLecerf GAbramov SZima EGao X(2016)Fast Polynomial Multiplication over F260Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation10.1145/2930889.2930920(255-262)Online publication date: 20-Jul-2016
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Recommendations

The integer transforms analogous to discrete trigonometric transforms

The fast generalized discrete Fourier transforms: a unified approach to the discrete sinusoidal transforms computation

Sliding discrete fractional transforms

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