An electronic device for generating a homomorphic ciphertext, includes: at least one processor, memory storing instructions that, when executed by the at least one processor, cause the electronic device to: identify one or more messages; encode each of the one or more messages to generate a first set and a second set each including one or more ciphertexts; output a third set corresponding to a multi-key by applying a public key based on the first set and the second set; and control generation of the first set and the second set and the output of the third set to operate with a complexity of O(n), wherein n is equal to a number of the one or more messages and a number of the one or more ciphertexts.