Paper 2018/785

Efficiently Processing Complex-Valued Data in Homomorphic Encryption

Carl Bootland, Wouter Castryck, Ilia Iliashenko, and Frederik Vercauteren


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 $X^m + b$. Our construction significantly reduces the noise growth in comparison to the original FV scheme, so much deeper arithmetic circuits can be homomorphically executed.

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Published elsewhere. Major revision. MathCrypt 2018
homomorphic encryptionencoding
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wouter castryck @ esat kuleuven be
2019-10-23: last of 2 revisions
2018-09-01: received
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      author = {Carl Bootland and Wouter Castryck and Ilia Iliashenko and Frederik Vercauteren},
      title = {Efficiently Processing Complex-Valued Data in Homomorphic Encryption},
      howpublished = {Cryptology ePrint Archive, Paper 2018/785},
      year = {2018},
      note = {\url{}},
      url = {}
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