Efficiently Processing Complex-Valued Data in Homomorphic Encryption
Carl Bootland, Wouter Castryck, Ilia Iliashenko, Fréderik Vercauteren
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.
Topics & Concepts
Homomorphic encryptionPlaintextGeneralizationScheme (mathematics)MathematicsEncryptionCryptographyPolynomialAdvanced Encryption StandardComputer scienceArithmeticDiscrete mathematicsTheoretical computer scienceAlgorithmMathematical analysisOperating systemCryptography and Data SecurityCryptography and Residue ArithmeticCoding theory and cryptography