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Efficiently processing complex-valued data in homomorphic encryption

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Abstract
We introduce a new homomorphic encryption scheme that is natively capable of computing with complex numbers. This is done by generalizing recent work of Chen, Laine, Player and Xia, who modified the Fan–Vercauteren scheme by replacing the integral plaintext modulus t by a linear polynomial X − b. Our generalization studies plaintext moduli of the form Xm + b. Our construction significantly reduces the noise growth in comparison to the original FV scheme, so much deeper arithmetic circuits can be homomorphically executed.
Keywords
homomorphic encryption, data encoding, 94A60, 68P25, 11T06, 11T22, 68P30

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Citation

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MLA
Bootland, Carl, et al. “Efficiently Processing Complex-Valued Data in Homomorphic Encryption.” JOURNAL OF MATHEMATICAL CRYPTOLOGY, vol. 14, no. 1, 2020, pp. 55–65, doi:10.1515/jmc-2015-0051.
APA
Bootland, C., Castryck, W., Iliashenko, I., & Vercauteren, F. (2020). Efficiently processing complex-valued data in homomorphic encryption. JOURNAL OF MATHEMATICAL CRYPTOLOGY, 14(1), 55–65. https://doi.org/10.1515/jmc-2015-0051
Chicago author-date
Bootland, Carl, Wouter Castryck, Ilia Iliashenko, and Frederik Vercauteren. 2020. “Efficiently Processing Complex-Valued Data in Homomorphic Encryption.” JOURNAL OF MATHEMATICAL CRYPTOLOGY 14 (1): 55–65. https://doi.org/10.1515/jmc-2015-0051.
Chicago author-date (all authors)
Bootland, Carl, Wouter Castryck, Ilia Iliashenko, and Frederik Vercauteren. 2020. “Efficiently Processing Complex-Valued Data in Homomorphic Encryption.” JOURNAL OF MATHEMATICAL CRYPTOLOGY 14 (1): 55–65. doi:10.1515/jmc-2015-0051.
Vancouver
1.
Bootland C, Castryck W, Iliashenko I, Vercauteren F. Efficiently processing complex-valued data in homomorphic encryption. JOURNAL OF MATHEMATICAL CRYPTOLOGY. 2020;14(1):55–65.
IEEE
[1]
C. Bootland, W. Castryck, I. Iliashenko, and F. Vercauteren, “Efficiently processing complex-valued data in homomorphic encryption,” JOURNAL OF MATHEMATICAL CRYPTOLOGY, vol. 14, no. 1, pp. 55–65, 2020.
@article{8665511,
  abstract     = {We introduce a new homomorphic encryption scheme that is natively capable of computing with complex numbers. This is done by generalizing recent work of Chen, Laine, Player and Xia, who modified the Fan–Vercauteren scheme by replacing the integral plaintext modulus t by a linear polynomial X − b. Our generalization studies plaintext moduli of the form Xm + b. Our construction significantly reduces the noise growth in comparison to the original FV scheme, so much deeper arithmetic circuits can be homomorphically executed.},
  author       = {Bootland, Carl and Castryck, Wouter and Iliashenko, Ilia and Vercauteren, Frederik},
  issn         = {1862-2976},
  journal      = {JOURNAL OF MATHEMATICAL CRYPTOLOGY},
  keywords     = {homomorphic encryption,data encoding,94A60,68P25,11T06,11T22,68P30},
  language     = {eng},
  number       = {1},
  pages        = {55--65},
  title        = {Efficiently processing complex-valued data in homomorphic encryption},
  url          = {http://dx.doi.org/10.1515/jmc-2015-0051},
  volume       = {14},
  year         = {2020},
}

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