Homomorphic encryption scheme

1. A method performed under control of a first device, the method comprising:

determining an enciphering function, based at least in part on a secret key of the first device and a system parameter;

enciphering a plaintext into a first ciphertext, based at least in part on the enciphering function;

transmitting, to a server, the first ciphertext and the system parameter;

transmitting, to a second device, a request to process the plaintext, wherein the first ciphertext, which corresponds to the plaintext, is processed to a second ciphertext by the second device, based at least in part on the request, and wherein the request includes a type of calculations to be performed on particular plaintext elements among multiple plaintext elements of the plaintext;

receiving, from the second device, the second ciphertext to which the first ciphertext has been processed by the second device without deciphering the first ciphertext wherein the transmission of the request to process the first ciphertext to the second ciphertext without deciphering the first ciphertext facilitates the plaintext to be hidden from the second device, to enable protection against attacks on the plaintext; and

deciphering the second ciphertext, based at least in part on the system parameter and a deciphering function.

2. The method of claim 1 , further comprising:

selecting the secret key and the system parameter.

3. The method of claim 1 , wherein at least one of: the secret key, the system parameter, the plaintext, the first ciphertext, the second ciphertext, the enciphering function, or the deciphering function is engaged in a non-associative octonion ring.

4. The method of claim 1 ,

wherein the deciphering the second ciphertext includes obtaining a process result of the plaintext.

5. The method of claim 1 , further comprising:

determining the deciphering function, based at least in part on the secret key and the system parameter.

6. The method of claim 1 , wherein the server is part of a cloud datacenter.

7. A method performed under control of a first device, the method comprising:

receiving, from a second device, a request to process a plaintext;

downloading, from a server and based at least in part on the received request, a system parameter and a first ciphertext that corresponds to the plaintext;

generating a second ciphertext by processing the first ciphertext, which corresponds to the plaintext, without deciphering the first ciphertext, based at least in part on the received request,

wherein processing the first ciphertext without deciphering the first ciphertext facilitates the plaintext to be hidden from the first device, which leads to protection attacks on the plaintext; and

transmitting, to the second device, the generated second ciphertext.

8. The method of claim 7 , wherein at least one of: the system parameter, the plaintext, the first ciphertext, or the second ciphertext is engaged in a non-associative octonion ring.

9. The method of claim 7 , wherein the plaintext is enciphered to the first ciphertext by the second device, based at least in part on the system parameter and a secret key of the second device.

10. A first device, comprising:

a function manager configured to determine an enciphering function, based at least in part on a secret key of the first device and a system parameter;

an encipherer, communicatively coupled to the function manager and configured to encipher, based at least in part on the enciphering function, a plaintext into a first ciphertext;

a transmitter, communicatively coupled to the encipherer and configured to transmit, to a server, the first ciphertext and the system parameter,

wherein the transmitter is further configured to transmit, to a second device, a request to process the plaintext, wherein the first ciphertext, which corresponds to the plaintext, is processed to a second ciphertext by the second device, based at least in part on the request, and wherein the request includes a type of calculations to be performed on particular plaintext elements among multiple plaintext elements of the plaintext;

a receiver, communicatively coupled to the transmitter and configured to receive, from the second device, the second ciphertext to which the first ciphertext has been processed by the second device without deciphering the first ciphertext,

wherein the transmission of the request to process the first ciphertext to the second ciphertext without deciphering the first ciphertext facilitates the plaintext to be hidden from the second device, to enable protection against attacks on the plaintext; and

a decipherer, communicatively coupled to the receiver and configured to decipher the second ciphertext, based at least in part on the system parameter and a deciphering function.

11. The first device of claim 10 , wherein the decipherer is further configured to obtain a process result of the plaintext.