Abstract: An encryption key generating method and apparatus based on homomorphic encryption, and a ciphertext operation method and apparatus using the generated encrypt key are disclosed. The method of generating an encryption key for performing encryption based on homomorphic encryption includes receiving data, generating a first encryption key and a second encryption key used for encrypting the data based on a secret key, and transmitting the first and second encryption keys.

Abstract: Disclosed is a homomorphic encryption operation apparatus and method. The homomorphic encryption operation method is performed by a computing device that includes processing hardware and storage hardware, and the method includes: receiving, and storing in the storage hardware, a ciphertext including modules; receiving, and storing in the storage hardware, an operation key including a relinearization key corresponding to the ciphertext; and performing, by the processing hardware, a homomorphic encryption operation on the ciphertext, wherein a modulus of the ciphertext is determined by the processing hardware based on a dimension of the modules and a number of the modules.

Abstract: An apparatus and method with homomorphic encryption are provided. A method for performing a homomorphic encryption operation may include generating a second ciphertext, having a second total number of dimensions, by performing a key switching operation using a key-switching key to generate the second ciphertext, encrypted by a second secret key, based on a homomorphic encrypted first ciphertext on a first modulus encrypted by a first secret key, where the first ciphertext has a first total number of dimensions, and generating a ciphertext on a second modulus by performing a blind rotation operation based on the second ciphertext and an operation key.

Abstract: A computing apparatus and method are provided. A homomorphic encryption operation method includes dividing a ciphertext having a first number of dimensions into a plurality of ciphertexts having a second number of dimensions, converting a secret key of each of the divided ciphertexts to a joint secret key by performing a key switching operation, generating new ciphertexts by applying the joint secret key to the divided ciphertexts, and performing a blind rotation operation based on the generated ciphertexts.

Abstract: An encoding method includes: receiving a plurality of messages; encoding the plurality of messages into a polynomial defined by multivariates; and encrypting the polynomial defined by the multivariates to generate a homomorphic ciphertext. The plurality of messages may be multidimensionally packed by using multivariates, and thus, an operation may be performed with low complexity in the process of matrix multiplication for ciphertexts packed with the multivariates.

Abstract: An apparatus with a homomorphic encryption operation includes: one or more processors configured to: generate a modified vector by preprocessing vector components of an operand ciphertext of a blind rotation operation based on an order of a polynomial of an output ciphertext of the blind rotation operation and a modulus of the operand ciphertext; and generate a homomorphic encryption operation result by performing the blind rotation operation based on a public key for performing the blind rotation operation and the modified vector.

Abstract: An apparatus including a receiver and a processor configured to generate a modulus switch ciphertext by performing modulus switching with respect to data received by the receiver, the modulus switching including mapping a component of an input ciphertext generated from the received data to an odd number, generate a blind rotated ciphertext by performing a blind rotation operation based on the modulus switched ciphertext, and generate encrypted data, as a homomorphic encryption operation result, by performing key switching based on the blind rotated ciphertext.

Abstract: Disclosed is a method and apparatus for modulus refresh, where the method for modulus refresh of a ciphertext in homomorphic encryption includes receiving a first ciphertext corresponding to a first modulus, generating a second ciphertext by performing a blind rotation on the first ciphertext, and generating a target ciphertext corresponding to a second modulus greater than the first modulus based on the first ciphertext and the second ciphertext.

Abstract: Disclosed are an apparatus and method with homomorphic encryption using automorphism. A computing apparatus includes one or more processors and a memory storing instructions configured to cause the one or more processors to, for a blind rotation key for performing a blind rotation operation and an operand ciphertext of the blind rotation operation: generate a preprocessed ciphertext by performing preprocessing on the operand ciphertext based on automorphism, and generate an operation result of the homomorphic encryption by performing the blind rotation operation for the operand ciphertext on a vector component of the preprocessed ciphertext and a vector component of the blind rotation key.

Abstract: A homomorphic encryption apparatus and method are disclosed. The homomorphic encryption apparatus includes one or more processors, and memory storing instructions configured to, when executed by the one or more processors, cause the one or more processors to receive a blind rotation key for performing a blind rotation operation and receive an operand ciphertext of the blind rotation operation, generate a first ciphertext by performing addition of a polynomial representation based on the blind rotation key and the operand ciphertext, and generate a target ciphertext by performing key switching and accumulative multiplication based on the first ciphertext.

Abstract: An encryption key generating method and apparatus based on homomorphic encryption, and a ciphertext operation method and apparatus using the generated encrypt key are disclosed. The method of generating an encryption key for performing encryption based on homomorphic encryption includes receiving data, generating a first encryption key and a second encryption key used for encrypting the data based on a secret key, and transmitting the first and second encryption keys.

Abstract: Disclosed is a method and apparatus for modulus refresh, where the method for modulus refresh of a ciphertext in homomorphic encryption includes receiving a first ciphertext corresponding to a first modulus, generating a second ciphertext by performing a blind rotation on the first ciphertext, and generating a target ciphertext corresponding to a second modulus greater than the first modulus based on the first ciphertext and the second ciphertext.

Abstract: An encoding method is disclosed. The present encoding method comprises the steps of: receiving a plurality of messages; encoding the plurality of messages into a polynomial expression having been multivariately defined, and encoding the multivariately defined polynomial expression so as to generate a homomorphic cyphertext.

Abstract: An operation apparatus and method for processing a homomorphic encrypted message are disclosed. The method includes producing an approximate polynomial corresponding to an operation function to be applied to a homomorphic encrypted message and approximately operating the homomorphic encrypted message using the approximate polynomial. Thus, an encrypted message may be efficiently processed.

Abstract: An operation apparatus and method for processing a homomorphic encrypted message are disclosed. The method includes producing an approximate polynomial corresponding to an operation function to be applied to a homomorphic encrypted message and approximately operating the homomorphic encrypted message using the approximate polynomial. Thus, an encrypted message may be efficiently processed.

Abstract: A drop emitting device that includes a drop generator, a drive signal including a plurality of fire intervals applied to the drop generator, wherein the drive signal includes in each fire interval a bi-polar drop firing waveform or a time varying non-firing waveform.

Abstract: A drop emitting device that includes a drop generator, a drive signal including a plurality of fire intervals applied to the drop generator, wherein the drive signal includes in each fire interval a bi-polar drop firing waveform or a time varying non-firing waveform.