Abstract: A processor-implemented method with homomorphic encryption includes: receiving a first ciphertext corresponding to a first modulus; generating a second ciphertext corresponding to a second modulus by performing modulus raising on the first ciphertext; and performing bootstrapping by encoding the second ciphertext using a commutative property and an associative property of operations included in a rotation operation.

Abstract: A processor-implemented method with homomorphic encryption includes: receiving a first ciphertext corresponding to a first modulus; generating a second ciphertext corresponding to a second modulus by performing modulus raising on the first ciphertext; and performing bootstrapping by encoding the second ciphertext using a commutative property and an associative property of operations included in a rotation operation.

Abstract: A method of performing a homomorphic permutation by a server includes: generating, via a ciphertext generation portion, a first ciphertext by adding noise to the basic ciphertext; transmitting, via a transmission portion, the first ciphertext to a client; performing, via an operation portion, a predetermined operation on the noise; receiving, via a reception portion, a second ciphertext from the client; and extracting, via an extraction portion, the basic ciphertext on which the predetermined operation is performed, by removing, from the second ciphertext, the noise on which the predetermined operation is performed, wherein the second ciphertext is a ciphertext that is re-encrypted by the client after decrypting the first ciphertext and performing the predetermined operation on the decrypted first ciphertext.

Abstract: A device for performing multi-key homomorphic encryption includes a public key generator configured to generate a public key by using a secret key for each client, and a multiplication key generator configured to generate a multiplication key by reusing a public key protection error used in the generating of the public key. By reducing the size of the multiplication key by reusing the public key protection error, the operation time and memory may be reduced.

Abstract: In a client-server model for generating a rotation operation key in fully homomorphic encryption, a client transmits a public key and a hierarchical Galois key generated using a secret key to a server, and the server performs a rotation operation on the public key using the hierarchical Galois key to directly generate one or more rotation operation keys, so that the server may generate a rotation operation key if necessary while computational burden and communication cost of the client are reduced.

Abstract: A homomorphic encryption operation key management system receives a public key and a hierarchical Galois key from a client device, verifies validity of a token in response to receiving the token and a request for a homomorphic encryption operation key for the client device from a server, and generates the homomorphic encryption operation key using the public key and the hierarchical Galois key and transmits the homomorphic encryption operation key to the server when the token is valid.

Abstract: Disclosed is an electronic apparatus. The electronic apparatus includes a memory storing a composite function in which at least two polynomials are composed and a processor configured to, based on a comparison operation command being received for a plurality of homomorphic ciphertexts, perform operation by reflecting the plurality of homomorphic ciphertexts to the composite function, and obtain a comparison result of the plurality of homomorphic ciphertexts based on the operation result, each of the at least two polynomials may output a value in a preset range for a value in a preset domain, and a domain of one of the at least two polynomials may be determined based on a range of a previous polynomial.

Abstract: An apparatus includes: one or more processors configured to: generate packed data by performing data packing on an encrypted image; and perform a homomorphic encryption operation based on the packed data and a weight.

Abstract: A processor-implemented encryption method using homomorphic encryption includes: receiving data; generating a ciphertext by encrypting the received data; determining a coefficient of an approximating polynomial for performing a modular reduction on a modulus corresponding to the ciphertext, based on an error between the approximating polynomial and a modular reduction function; and performing bootstrapping on the ciphertext by performing the modular reduction based on the determined coefficient of the approximating polynomial.

Abstract: An encryption method and apparatus based on homomorphic encryption using a composition of functions. The encryption method includes generating a ciphertext by encrypting data, and bootstrapping the ciphertext by performing a modular reduction based on a composition of a function for a modulus corresponding to the ciphertext.

Abstract: A method and apparatus for processing a ciphertext based on homomorphic encryption. The method includes determining an approximate polynomial corresponding to a modulus reduction for bootstrapping a ciphertext based on samples extracted from the modulus reduction, and bootstrapping the ciphertext based on the approximate polynomial.

Abstract: Provided are an electronic device for sorting homomorphic ciphertext by using shell sorting and an operating method thereof to sort ciphertext generated by using homomorphic encryption according to a size of an original number corresponding thereto.

Abstract: Provided is a method for generating a fully homomorphic code, which includes: generating an Idempotent polynomial; and generating a fully homomorphic code message by using the generated Idempotent polynomial and a message.

Abstract: A processor-implemented method with homomorphic encryption includes: receiving a first ciphertext corresponding to a first modulus; generating a second ciphertext corresponding to a second modulus by performing modulus raising on the first ciphertext; and performing bootstrapping by encoding the second ciphertext using a commutative property and an associative property of operations included in a rotation operation.

Abstract: Disclosed is an electronic apparatus. The electronic apparatus includes a memory storing a composite function in which at least two polynomials are composed and a processor configured to, based on a comparison operation command being received for a plurality of homomorphic ciphertexts, perform operation by reflecting the plurality of homomorphic ciphertexts to the composite function, and obtain a comparison result of the plurality of homomorphic ciphertexts based on the operation result, each of the at least two polynomials may output a value in a preset range for a value in a preset domain, and a domain of one of the at least two polynomials may be determined based on a range of a previous polynomial.

Abstract: A processor-implemented encryption method using homomorphic encryption includes: receiving data; generating a ciphertext by encrypting the received data; determining a coefficient of an approximating polynomial for performing a modular reduction on a modulus corresponding to the ciphertext, based on an error between the approximating polynomial and a modular reduction function; and performing bootstrapping on the ciphertext by performing the modular reduction based on the determined coefficient of the approximating polynomial.

Abstract: Provided are an electronic device for sorting homomorphic ciphertext by using shell sorting and an operating method thereof to sort ciphertext generated by using homomorphic encryption according to a size of an original number corresponding thereto.

Abstract: Disclosed is an encryption method and apparatus. The encryption method using homomorphic encryption may include generating a ciphertext by encrypting data, and bootstrapping the ciphertext by performing a modular reduction based on a selection of one or more target points for a modulus corresponding to the ciphertext.

Abstract: An encryption method and apparatus based on homomorphic encryption using a composition of functions. The encryption method includes generating a ciphertext by encrypting data, and bootstrapping the ciphertext by performing a modular reduction based on a composition of a function for a modulus corresponding to the ciphertext.

Abstract: A method and apparatus for processing a ciphertext based on homomorphic encryption. The method includes determining an approximate polynomial corresponding to a modulus reduction for bootstrapping a ciphertext based on samples extracted from the modulus reduction, and bootstrapping the ciphertext based on the approximate polynomial.