Data processing method and device based on homomorphic encryption
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.
1 . An electronic device for generating a homomorphic ciphertext, comprising:
at least one processor including processing circuitry, and
memory comprising one or more storage media storing instructions that, when executed by the at least one processor individually or collectively, 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; and
output a third set corresponding to a multi-key by applying a public key based on the first set and the second set,
wherein generation of the first set and the second set and the output of the third set are controlled to operate with a complexity of O(n), and
wherein n is equal to a number of the one or more messages or a number of the one or more ciphertexts.
2 . The electronic device of claim 1 , wherein the first set and the second set are each decryptable with one or more secret keys, respectively,
wherein the public key is configured by one or more public keys, and
wherein a number of the one or more secret keys and a number of the one or more public keys are equal to the number of the one or more messages.
3 . The electronic device of claim 1 , wherein the third set is an output value for a first computation configured by a product of a first ciphertext of the first set and a second ciphertext of the second set.
4 . The electronic device of claim 1 , wherein a first computation of a first ciphertext of the first set and a second computation of a second ciphertext of the second set follow homomorphic attributes of gadget decomposition.
5 . The electronic device of claim 1 , wherein the first set and the second set are input ciphertexts of a multi-key BFV scheme of CDKS.
6 . The electronic device of claim 5 , wherein the first set and the second set are input ciphertexts of a multi-key CKKS scheme of the CDKS.
7 . The electronic device of claim 1 , wherein the third set is calculated by a tensor product and re-linearization of the first set and the second set.
8 . A method for generating a homomorphic ciphertext by an electronic device, comprising:
identifying one or more messages;
encoding each of the one or more messages to generate a first set and a second set each including one or more ciphertexts; and
outputting a third set corresponding to a multi-key by applying a public key based on the first set and the second set,
wherein generation of the first set and the second set and the outputting the third set operate in a complexity of O(n), and
wherein n is equal to a number of the one or more messages and a number of the one or more ciphertexts.
9 . The method of claim 8 , wherein the first set and the second set are each decryptable with one or more secret keys, respectively,
the public key is configured by one or more public keys, and
wherein a number of the one or more secret keys and a number of the one or more public keys are equal to the number of the one or more messages.
10 . The method of claim 8 , wherein the third set is an output value of a first computation configured by a product of a first ciphertext of the first set and a second ciphertext of the second set.
11 . The method of claim 8 , wherein a first computation of a first ciphertext of the first set and a second computation of a second ciphertext of the second set follow homomorphic attributes of gadget decomposition.
12 . The method of claim 8 , wherein the first set and the second set are input ciphertexts of a multi-key BFV scheme of CDKS.
13 . The method of claim 8 , wherein the first set and the second set are input ciphertexts of a multi-key CKKS scheme of CDKS.
14 . The method of claim 8 , wherein the third set is calculated by a tensor product and re-linearization of the first set and the second set.
15 . A non-transitory computer readable medium storing instructions that, when executed by at least one processor of an electronic device, 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; and
output a third set corresponding to a multi-key by applying a public key based on the first set and the second set,
wherein generation of the first set and the second set and the output of the third set are controlled to operate with a complexity of O(n), and
wherein n is equal to a number of the one or more messages or a number of the one or more ciphertexts.