Abstract: Some embodiments are directed to a computer-implemented method to convert a first computation network of operations into a second computation network of operations. The operations of the second computation network being fully homomorphic encrypted (FHE) operations. The converting may include obtaining for the input values of the operation a supported range of the input value in the first computation network, and determining a prescribed range for the input values of a corresponding FHE operation.

Abstract: The invention relates to a cryptographic method and variants thereof based on homomorphic encryption enabling the evaluation of univariate or multivariate real-valued functions on encrypted data, in order to allow carrying out homomorphic processing on encrypted data more broadly and efficiently.

Abstract: Some embodiments are directed to a computer-implemented blind rotation method for use in fully homomorphic encryption (FHE). The method comprises rotating a polynomial (210) over a masked value and iterating over secret key digits, e.g., they may be ternary. The secret key digits can have at least three different values. An iteration further blind rotating the polynomial as indicated by a current secret key digit and a corresponding masking value. In the iteration an encrypted multiplier polynomial may be computed from bootstrapping keys and the masking values. One external product may be done in an iteration with the encrypted multiplier polynomial to further blind rotate the polynomial.

Abstract: Some embodiments are directed to a cryptographic encrypted computation method (400). The method involves performing a blind rotation of a ciphertext according to a test polynomial. The blind rotation results in an encrypted polynomial product of the test polynomial and a bootstrapping monomial represents the plaintext value as an exponent, modulo a modulus (q) and modulo a quotient polynomial (p(X)). . . . The quotient polynomial p(X) divides a number-theoretic transform (NTT) polynomial XM?1 that allows a number-theoretic transform modulo the modulus q, e.g., q is a power of two and p(X)=XN+XN/2+1. The blind rotation is performed using the NTT, while the test polynomial is defined in such a way that the polynomial product is programmed to have desired output values for respective plaintext values as a fixed coefficient.

Abstract: The invention relates to a cryptographic method and variants thereof based on homomorphic encryption enabling the evaluation of real-valued functions on encrypted data, in order to allow carrying out homomorphic processing on encrypted data more broadly and efficiently.

Abstract: Some embodiments are directed to a computer-implemented method of determining encrypted computation parameters for carrying out an encrypted computation on noisy ciphertexts. A computation graph is divided into multiple subgraphs, defined by a type and by instantiation parameters for the type. Respective sets of encrypted computation parameters are defined for the respective types. An optimization of the encrypted computation parameters is performed to minimize a computational cost of carrying out the encrypted computation according to the encrypted computation parameters. The encrypted computation parameters are constrained to satisfy a noise constraint on ciphertext noise while carrying out the encrypted computation. The noise constraint is based on respective noise constraints for respective subgraphs, defined by a noise constraint function for the type that takes at least the encrypted computation parameters for the type and the instantiation parameters of the subgraph as input.

Abstract: Some embodiments are directed to a computer-implemented method for converting a first computation network of operations arranged to compute a function into a second computation network of FHE operations arranged to compute the same function. For example, a set of expansion factors (?i) may be determined for matrix operations in the first computation network. Real-valued matrices may be converted by scaling the real-valued matrices with their corresponding expansion factor and rounding. An accuracy measure for the second computation network can be iteratively optimized.

Abstract: Some embodiments are directed to a computer-implemented method (500) of determining a set of coefficients for homomorphically multiplying an encrypted value by a scalar. The encrypted value is represented by multiple respective value ciphertexts encrypting the value multiplied by respective powers of an even radix. The scalar multiplication is performed as a linear combination of the multiple respective value ciphertexts according to the set of coefficients. The set of coefficients are determined as digits of a radix decomposition of the scalar with respect to the radix. The determined digits lie between minus half the radix, inclusive, and plus half the radix, inclusive. It is ensured that no two subsequent digits are both equal in absolute value to half the radix.

Abstract: Some embodiments are directed to a fully homomorphic encryption (FHE) cryptography, wherein some encrypted data items are clipped, thereby reducing a bit-size of the encrypted data item and increasing an associated noise level of the encrypted data item. An FHE operation or a decrypt operation that operates on the clipped encrypted data item as input, has noise tolerance above a noise level associated with the clipped encrypted data item.