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.

An accelerator includes polynomial multiplier circuitry including at least one modulus multiplier operating according to a mode. The at least one modulus multiplier include a multiplier to multiply two polynomial coefficients to generate a multiplication result, a power of two reducer to reduce the multiplication result to a reduced multiplication result when the mode is a power of two mode, and a prime modulus reducer to reduce the multiplication result to the reduced multiplication result when the mode is a prime modulus mode.

Content, such as an encryption key, may be transmitted between computing systems that both use more than one encryption algorithm. Secrets may be used to encode the content. The different encryption algorithms may be used to separately encrypt the encoded content and the secrets prior to communicating the encrypted, encoded content and encrypted secrets between computing systems.

A range determination unit (412) takes as input an input ciphertext C.sub.i resulting from encrypting input data, determines whether a value obtained from the input data is within a reference range, and generates a range ciphertext a.sub.j depending on a determined result. A result generation unit (413) performs a homomorphic operation on the range ciphertext a.sub.j generated by the range determination unit (412), so as to generate a result ciphertext D of a result of performing inference including a non-polynomial operation on the input data. An output unit (414) outputs the result ciphertext D.

Disclosed is a method of generating digital signature information comprising: receiving a message; computing a particular solution in which a result of calculating the particular solution in a public key becomes a function-processed output value predetermined in the received message; and generating digital signature information for the message using the computed particular solution, wherein the public key is computed using a ring having a dimension (d) represented by a power of 2 and an integer multiplication of 3 or more.

A PQ signature scheme MMSAT that is capable of aggregating and compressing unrelated messages signed individually by different parties. The scheme extends the notion of multi-signatures, which are signatures that support aggregation of signatures on a single message signed by multiple parties.

The invention includes a tool for the generation and usage of a dynamic polychrome lattice image for unique and secure authentication and verification purposes. The tool is multi-purposed and can be applied to a variety of use cases and may utilize multiple channels of communication between devices. The dynamic polychrome lattice image may be adjusted according to the display size and resolution of various user devices. System devices may scan the dynamic polychrome lattice image, and upon successful retrieval and decryption of the dynamic polychrome lattice image, the user may be authenticated and verified to access one or more programs or services.

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.

Disclosed herein are a method for generating Gaussian error data using flash memory and an apparatus using the method. The method includes receiving a request to generate Gaussian error data and delivering an operation command to flash memory; generating Gaussian error noise based on a threshold voltage that is generated when the flash memory performs the operation command; and generating Gaussian error data so as to correspond to the Gaussian error noise and providing the same.

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.