Aspects of the present disclosure involve a method, a system and a computer readable memory to perform a cryptographic operation that includes identifying a first set of mutually coprime numbers, obtaining a second set of input numbers coprime with a corresponding one of the first set of mutually coprime numbers, obtaining an output number that is a weighted sum of the second set of input numbers, each of the second set of input numbers being taken with a weight comprising a product of all of the first set of mutually coprime numbers except the corresponding one of the first set of mutually coprime numbers, and performing the cryptographic operation using the output number.

Methods, systems, and computer programs for generating cryptographic function parameters are described. In some examples, source code that defines seed information and a pseudorandom function is accessed. A parameter for a cryptographic function by operation of one or more data processors is generated. The parameter is generated from the seed information and the pseudorandom function. The parameter has a larger size in memory than the source code that defines the seed information and the pseudorandom function.

A method may include collecting from each of multiple endpoint devices a set of anonymized interactions of the corresponding endpoint device with other endpoint devices. Each anonymized interaction in the set of anonymized interactions may be based on an ephemeral unique identifier of another endpoint device involved in a corresponding anonymized interaction with the corresponding endpoint device. The method may include, for each endpoint device, resolving identities of the other endpoint devices with which the corresponding endpoint device has interacted from the corresponding set of anonymized interactions.

Methods, systems, and computer programs for generating cryptographic function parameters are described. In some examples, astronomical data from an observed astronomical event is obtained. A pseudorandom generator is seeded based on the astronomical data. After seeding the pseudorandom generator, an output from the pseudorandom generator is obtained. A parameter for a cryptographic function is generated by operation of one or more data processors. The parameter is generated from the output from the pseudorandom generator.

A system for generating and managing virtual reality identification (ID) based on real-world personal information includes a user terminal that requests issuance of a virtual ID generated based on real-world personal information and participates in a metaverse virtual space with the virtual ID, and a virtual ID generation and management unit that generates and issues the virtual ID based on the real-world personal information provided by the user terminal and authenticates the validity of the virtual ID when linked to the metaverse virtual space by the user terminal.

Methods, systems, and computer programs for generating cryptographic function parameters are described. In some examples, source code that defines seed information and a pseudorandom function is accessed. A parameter for a cryptographic function by operation of one or more data processors is generated. The parameter is generated from the seed information and the pseudorandom function. The parameter has a larger size in memory than the source code that defines the seed information and the pseudorandom function.

A process receives a specification of a finite-state machine and an encrypted language element of a language over an input alphabet for the finite-state machine. The received encrypted language element is encrypted with a selected public key of a plurality of public keys. The process decrypts the encrypted language element using each private key of a plurality of private keys corresponding to the public keys. The decrypting provides a plurality of decrypted language elements and the process applies each decrypted language element to the finite-state machine. The process identifies a decrypted language element that that is accepted by the finite-state machine. The process identifies a private key, of the private keys, used in the decrypting that provided the decrypted language element identified as being accepted by the finite-state machine. The process receives from the message sender an encrypted message, and uses the identified private key in decrypting the encrypted message.

Methods, systems, and computer programs for generating cryptographic function parameters are described. In some examples, astronomical data from an observed astronomical event is obtained. A pseudorandom generator is seeded based on the astronomical data. After seeding the pseudorandom generator, an output from the pseudorandom generator is obtained. A parameter for a cryptographic function is generated by operation of one or more data processors. The parameter is generated from the output from the pseudorandom generator.

The present invention involves with a method of searchable public-key encryption, a system and server using the method.

A process selects a public key from a plurality of public keys provided by a message recipient that is to receive an encrypted message. The process establishes an input alphabet for a finite-state machine. The process further constructs the finite-state machine and a language over the input alphabet such that the finite-state machine accepts the language, where the language includes language elements. The process encrypts a language element of the language using the selected public key to provide an encrypted language element. The process electronically transmits the encrypted language element and a specification of the finite-state machine to the message recipient for securely identifying the selected public key to the message recipient. The process encrypts a message using the selected public key to provide the encrypted message. The process also electronically transmits the encrypted message to the message recipient.