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Homomorphic SIM2D operations : single instruction much more data

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Abstract
In 2014, Smart and Vercauteren introduced a packing technique for homomorphic encryption schemes by decomposing the plain-text space using the Chinese Remainder Theorem. This technique allows to encrypt multiple data values simultaneously into one ciphertext and execute Single Instruction Multiple Data operations homomorphically. In this paper we improve and generalize their results by introducing a flexible Laurent polynomial encoding technique and by using a more fine-grained CRT decomposition of the plaintext space. The Laurent polynomial encoding provides a convenient common framework for all conventional ways in which input data types can be represented, e.g. finite field elements, integers, rationals, floats and complex numbers. Our methods greatly increase the packing capacity of the plaintext space, as well as one's flexibility in optimizing the system parameters with respect to efficiency and/or security.
Keywords
ENCRYPTION

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MLA
Castryck, Wouter, et al. “Homomorphic SIM2D Operations : Single Instruction Much More Data.” ADVANCES IN CRYPTOLOGY : EUROCRYPT 2018, PT I, edited by Jesper Buus Nielsen and Vincent Rijmen, vol. 10820, Springer, 2018, pp. 338–59, doi:10.1007/978-3-319-78381-9_13.
APA
Castryck, W., Iliashenko, I., & Vercauteren, F. (2018). Homomorphic SIM2D operations : single instruction much more data. In J. B. Nielsen & V. Rijmen (Eds.), ADVANCES IN CRYPTOLOGY : EUROCRYPT 2018, PT I (Vol. 10820, pp. 338–359). Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-78381-9_13
Chicago author-date
Castryck, Wouter, Ilia Iliashenko, and Frederik Vercauteren. 2018. “Homomorphic SIM2D Operations : Single Instruction Much More Data.” In ADVANCES IN CRYPTOLOGY : EUROCRYPT 2018, PT I, edited by Jesper Buus Nielsen and Vincent Rijmen, 10820:338–59. Cham, Switzerland: Springer. https://doi.org/10.1007/978-3-319-78381-9_13.
Chicago author-date (all authors)
Castryck, Wouter, Ilia Iliashenko, and Frederik Vercauteren. 2018. “Homomorphic SIM2D Operations : Single Instruction Much More Data.” In ADVANCES IN CRYPTOLOGY : EUROCRYPT 2018, PT I, ed by. Jesper Buus Nielsen and Vincent Rijmen, 10820:338–359. Cham, Switzerland: Springer. doi:10.1007/978-3-319-78381-9_13.
Vancouver
1.
Castryck W, Iliashenko I, Vercauteren F. Homomorphic SIM2D operations : single instruction much more data. In: Nielsen JB, Rijmen V, editors. ADVANCES IN CRYPTOLOGY : EUROCRYPT 2018, PT I. Cham, Switzerland: Springer; 2018. p. 338–59.
IEEE
[1]
W. Castryck, I. Iliashenko, and F. Vercauteren, “Homomorphic SIM2D operations : single instruction much more data,” in ADVANCES IN CRYPTOLOGY : EUROCRYPT 2018, PT I, Tel Aviv, Israel, 2018, vol. 10820, pp. 338–359.
@inproceedings{8568119,
  abstract     = {In 2014, Smart and Vercauteren introduced a packing technique for homomorphic encryption schemes by decomposing the plain-text space using the Chinese Remainder Theorem. This technique allows to encrypt multiple data values simultaneously into one ciphertext and execute Single Instruction Multiple Data operations homomorphically. In this paper we improve and generalize their results by introducing a flexible Laurent polynomial encoding technique and by using a more fine-grained CRT decomposition of the plaintext space. The Laurent polynomial encoding provides a convenient common framework for all conventional ways in which input data types can be represented, e.g. finite field elements, integers, rationals, floats and complex numbers. Our methods greatly increase the packing capacity of the plaintext space, as well as one's flexibility in optimizing the system parameters with respect to efficiency and/or security.},
  author       = {Castryck, Wouter and Iliashenko, Ilia and Vercauteren, Frederik},
  booktitle    = {ADVANCES IN CRYPTOLOGY : EUROCRYPT 2018, PT I},
  editor       = {Nielsen, Jesper Buus and Rijmen, Vincent},
  isbn         = {9783319783802},
  issn         = {0302-9743},
  keywords     = {ENCRYPTION},
  language     = {eng},
  location     = {Tel Aviv, Israel},
  pages        = {338--359},
  publisher    = {Springer},
  title        = {Homomorphic SIM2D operations : single instruction much more data},
  url          = {http://dx.doi.org/10.1007/978-3-319-78381-9_13},
  volume       = {10820},
  year         = {2018},
}

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