Abstract: Some embodiments are directed to a computer-implemented encrypted computation method (500). The method operates on a ciphertext that comprises one or more random mask polynomials and a body polynomial. which is derived from the mask polynomials and a plaintext. The mask and body polynomials of the ciphertext are multiplied by respective multiplicand polynomials. for example. as part of a programmable bootstrapping of a TFHE-like fully homomorphic encryption scheme. To perform this multiplication efficiently. the ciphertext is stored by storing a seed of pseudo-random number generator and a representation of the body polynomial in a Fourier domain of a number-theoretic transform. To perform the multiplication, the ciphertext is expanded by using the pseudo-random number generator according to the seed to generate representations of the mask polynomials in the Fourier domain. The multiplications can then be performed efficiently in the Fourier domain.

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 an 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 made more efficient by 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.