Method and device for multi-key homomorphic encryption

A device for performing multi-key homomorphic encryption, the device comprising:

• memory storing one or more instructions;
• and
• one or more processors;
• wherein the one or more instructions, when executed by the one or more processors, cause the device to:
• generate a secret key;
• select a public key protection error from an error distribution;
• generate a public key based on the secret key and the public key protection error;
• select a multiplication key protection error from the error distribution;
• generate a multiplication key based on the secret key, the public key protection error, and the multiplication key protection error, wherein the multiplication key is generated by using a modified Ring Learning with Error (RLWE) sample, and wherein the modified RLWE sample is defined in the form of (α, −αs+x, αx+e), where a denotes an element selected from a uniform distribution on Rq, s denotes a secret key distribution, and x and e denote an error distribution;
• receive, from at least one client, a ciphertext encrypted using the public key;
• perform a homomorphic operation on the ciphertext using the multiplication key to obtain a resulting ciphertext;
• and
• transmit the resulting ciphertext to the at least one client.

A method of performing multi-key homomorphic encryption, the method comprising:

• generating a public key based on a secret key for each of a plurality of clients;
• generating corresponding multiplication keys for the plurality of clients by reusing public key protection errors used in the generating of the public keys, wherein a multiplication key is generated using a modified Ring Learning with Error (RLWE) sample, and wherein the modified RLWE sample is defined in the form of (α, −αs+x, αx+e), where a denotes an element selected from a uniform distribution on Rq, s denotes a secret key distribution, and x and e denote an error distribution;
• receiving, from the plurality of clients, ciphertexts encrypted using corresponding public keys;
• performing homomorphic operations on the ciphertexts using the corresponding multiplication keys to obtain resulting ciphertexts;
• and
• transmitting the resulting ciphertexts to the plurality of clients.

A non-transitory computer-readable recording medium having one or more instructions recorded thereon, that, when executed by one or more processors, cause the one or more processors to:

• generate a public key based on a secret key for each of a plurality of clients;
• generate corresponding multiplication keys for the plurality of clients by reusing public key protection errors used in the generating of the public keys, wherein a multiplication key is generated using a modified Ring Learning with Error (RI WE) sample, and wherein the modified RLWE sample is defined in the form of (α, −αs+xαx+e), where a denotes an element selected from a uniform distribution on Rq, s denotes a secret key distribution, and x and e denote an error distribution;
• receive, from the plurality of clients, ciphertexts encrypted using corresponding public keys;
• perform homomorphic operations on the ciphertexts using the corresponding multiplication keys to obtain resulting ciphertexts;
• and
• transmit the resulting ciphertexts to the plurality of clients.