A method of executing a program operating on data encrypted by a homomorphic encryption. Execution of a program instruction includes the homomorphic evaluation of an associated function in the ciphertext space, homomorphic masking of the result of the evaluation with a previously encrypted random sequence, decryption of the evaluation result thus masked followed by a new encryption and then homomorphic unmasking in the ciphertext space. The result of execution of the instruction does not appear in plain text at any time during execution of the instruction.