Abstract: A method may include obtaining a common reference string. The method may further include obtaining a first public key for a first party and a second public key for a second party. The method may also include obtaining a first encrypted message, the first encrypted message encrypted using the first public key. The method may further include obtaining a second encrypted message, the second encrypted message encrypted using the second public key. The method may also include obtaining a proof. The method may further include verifying, using the proof, the common reference string, the first public key, and the second public key, that a decryption of the first encrypted message and a decryption of the second encrypted message are equivalent without decrypting the first encrypted message and without decrypting the second encrypted message.

Abstract: A method may include obtaining public keys for each user of a set of users, where each user is associated with a unique public key and a unique private key. The method may also include obtaining a designated set of users, where the designated set of users is a subset of the set of users. The method may additionally include generating, using the public keys, a digest associated with the designated set of users. The digest includes reduced data sets in a secure form, where each user of the set of users is associated with one of the reduced data sets that is indicative of whether the user is in the designated set of users, and the reduced data set is accessible using the private key of the user. The method may also include posting the digest to a location accessible from an electronic device of the user.

Abstract: A system may include a communication device configured to communicate over a network, one or more processors, and one or more non-transitory computer-readable media containing instructions that, when executed by the one or more processors, cause the system to perform one or more operations. The operations may include performing a cryptographic operation on one or more packets to facilitate secure communication between the system and a computing device over the network, the cryptographic operation including probabilistic rounding. The operations may also include communicating, via the communication device, with the computing device over the network using the one or more packets.

Abstract: A method may include extracting feature-data from an image which includes location data that indicates multiple locations within the image and multiple feature vectors that each correspond to one of the multiple locations. Each feature vector may represent a feature of an object in the image. The method may include determining a feature-data plot based on relative positions of the multiple locations and selecting a grid for the feature-data plot. The method may include generating a first representative feature vector for a first cell of the grid based on a first feature vector set and generating a second representative feature vector for a second cell of the grid based on a second feature vector set. The method may include generating a single feature vector that represents the object in the image based on the first representative feature vector and the second representative feature vector and encrypting the single feature vector.

Abstract: A method of equality verification using relational encryption including receiving a relational key that includes a first relational key component and a registration ciphertext that includes an encryption of a first plaintext data set. The method includes storing the registration ciphertext without decrypting the registration ciphertext. After the storing of the registration ciphertext, the method includes receiving an authentication request and communicating a safeguard data set that includes a random challenge in response to the authentication request. The method includes receiving an encrypted response that is generated based on the safeguard data set and a second plaintext data set. The method includes verifying a relationship between the encrypted response and the registration ciphertext using the relational key without decrypting the encrypted response and without decrypting the registration ciphertext. The relationship indicates that equality exists between the first and the second plaintext data sets.

Abstract: An anonymization system may include a merger to merge a public database and a private database to create a merged database. The merged database may include multiple blank entries and multiple initial values associated with multiple user identifiers. The anonymization system may include a value generator to fill values for the blank entries via a machine learning algorithm and based on the initial values to create a filled database including the initial values and the fill values. The anonymization system may include a perturber to perturb one or more of the initial values or the fill values of the filled database to create a perturbed database. The anonymization system may include a releaser to release at least a portion of the perturbed database.

Abstract: A method may include generating, via a setup function, public parameters associated with a random updatable function. The method may further include generating, via an initialization function and based at least in part on the public parameters generated by the setup function, a first random element and a first state. The method may further include generating, via an update function and based at least in part on the public parameters generated by the setup function, a third random element and a second state. Inputs of the update function may include the first state generated by the initialization function and a second random element.

Abstract: A method includes receiving a first biometric data set representative of a first biometric sample provided by a user and public parameters. The method includes generating a first set of exchange information based thereon and communicating it to a system server. The method includes receiving a second set of exchange information based on the public parameters and a second biometric data set representative of a second biometric sample and is symmetric with respect to the first set of exchange information. The method includes computing a session key for the communication session by applying a first hash function based on a hash key to a subset of the second set of exchange information and a second hash function based on a projected key to a subset of the first set of exchange information. The method includes using the session key in communications during the communication session.

Abstract: A method of enabling digital currency transfers subject to a policy may include generating a master secret key and an associated master verification key. A raw selective secret key and an associated raw selective verification key may be generated. A first signature based on the policy and the raw selective verification key may be encrypted using the master secret key. A selective secret key may be generated based on the raw selective secret key. A selective verification key may be generated based on the policy and the first signature. A second signature based on a message and the policy may be encrypted using the selective secret key.

Abstract: A method includes generating a secret key for encryption and decoding data. The method includes identifying a set of data in plaintext format. The method further includes converting, by a processing device, the data in plaintext format to ciphertext using a polynomial. The method also includes sending the ciphertext to a remote device for data processing, wherein the remote device is to process the ciphertext without having the secret key. The method includes receiving processed ciphertext from the remote device. The method further includes decoding, by the processing device, the processed ciphertext based on the secret key and the polynomial to yield processed plaintext. The method also includes outputting the processed plaintext.

Abstract: A method of biometric authentication includes receiving a biometric input from a user for authentication of the user to access a system. The method includes receiving a set of elements of a field and a random number from an authentication server via a network. The method further includes decoding the biometric input based on the set of elements to generate a polynomial. The method also includes generating a signature key based on the polynomial. The method includes signing the random number with the signature key. The method includes sending the signed random number to the authentication server. The method further includes restricting access to the system until the user is authenticated by the authentication server. The method also includes permitting access to the system in response to receiving an authentication message from the authentication server.

Abstract: A method of participation verification includes generating sets of cryptocurrency coins (coin sets). The coin sets have cryptocurrency coins and correlate to events for which participation is verified. The method includes generating user keys including unique public keys for each user and user secret keys. The method includes assigning a public key to a user, communicating the assigned public key to a user device and enabling download of a verification application. The method includes receiving a first coin request that includes identification of a first coin set, the assigned public key, and a data set. The method includes verifying user participation in an event based on the data set. The method includes executing a cryptocurrency transaction with the user device. The cryptocurrency transaction including public validation of a transfer of a cryptocurrency coin from the identified coin set to the user device via an append-only ledger.

Abstract: A method includes receiving a first message that includes a first relational key element based on a first group element, and a second relational key element based on the first group element and raised to the power of a first plaintext value. The method also includes receiving a second message that includes a third relational key element based on a second group element, and a fourth relational key element based on the second group element and raised to the power of a second plaintext value. The method additionally includes comparing the first message to the second message without decryption of the first or second messages and, based on the comparison, determining that the first plaintext value and the second plaintext value are the same.

Abstract: A method includes receiving biometric data, the biometric data non-uniformly distributed and processing the biometric data to a level of randomness as a plaintext vector, the level of randomness associated with a security level. The method also includes encrypting the plaintext vector using a relational linearity encryption scheme to generate a linearity ciphertext representative of the plaintext vector, encrypting the plaintext vector using a relational proximity encryption scheme to generate a proximity ciphertext representative of the plaintext vector, and communicating the linearity ciphertext and the proximity ciphertext to an authentication server.

Abstract: A method includes receiving a first message that includes a first relational key element based on a first group element, and a second relational key element based on the first group element and raised to the power of a first plaintext value. The method also includes receiving a second message that includes a third relational key element based on a second group element, and a fourth relational key element based on the second group element and raised to the power of a second plaintext value. The method additionally includes comparing the first message to the second message without decryption of the first or second messages and, based on the comparison, determining that the first plaintext value and the second plaintext value are the same.

Abstract: A method includes receiving a first and a second linearity ciphertexts representative of a first and second biometric templates, respectively that are encrypted using a relational linearity encryption scheme (linearity scheme). The linearity scheme is based on learning parity with noise. The method includes discovering a linearity relationship between the first and the second linearity ciphertexts. The method includes receiving a first and a second proximity hash value representative of the first and second biometric templates, respectively encrypted using a relational proximity hash scheme (proximity scheme). The proximity scheme is based on the linearity scheme and an error correcting code. The method includes detecting a proximity between the first and the second proximity hash value in terms of a Hamming distance. The method includes authenticating an identity of a user based on the proximity and the linearity relationship.

Abstract: A method includes receiving biometric data, the biometric data non-uniformly distributed and processing the biometric data to a level of randomness as a plaintext vector, the level of randomness associated with a security level. The method also includes encrypting the plaintext vector using a relational linearity encryption scheme to generate a linearity ciphertext representative of the plaintext vector, encrypting the plaintext vector using a relational proximity encryption scheme to generate a proximity ciphertext representative of the plaintext vector, and communicating the linearity ciphertext and the proximity ciphertext to an authentication server.

Abstract: A method includes receiving a first and a second linearity ciphertexts representative of a first and second biometric templates, respectively that are encrypted using a relational linearity encryption scheme (linearity scheme). The linearity scheme is based on learning parity with noise. The method includes discovering a linearity relationship between the first and the second linearity ciphertexts. The method includes receiving a first and a second proximity hash value representative of the first and second biometric templates, respectively encrypted using a relational proximity hash scheme (proximity scheme). The proximity scheme is based on the linearity scheme and an error correcting code. The method includes detecting a proximity between the first and the second proximity hash value in terms of a Hamming distance. The method includes authenticating an identity of a user based on the proximity and the linearity relationship.

Abstract: A method includes receiving biometric data, the biometric data non-uniformly distributed and processing the biometric data to a level of randomness as a plaintext vector, the level of randomness associated with a security level. The method also includes encrypting the plaintext vector using a relational linearity encryption scheme to generate a linearity ciphertext representative of the plaintext vector, encrypting the plaintext vector using a relational proximity encryption scheme to generate a proximity ciphertext representative of the plaintext vector, and communicating the linearity ciphertext and the proximity ciphertext to an authentication server.

Abstract: A method of equality verification using relational encryption including receiving a relational key that includes a first relational key component and a registration ciphertext that includes an encryption of a first plaintext data set. The method includes storing the registration ciphertext without decrypting the registration ciphertext. After the storing of the registration ciphertext, the method includes receiving an authentication request and communicating a safeguard data set that includes a random challenge in response to the authentication request. The method includes receiving an encrypted response that is generated based on the safeguard data set and a second plaintext data set. The method includes verifying a relationship between the encrypted response and the registration ciphertext using the relational key without decrypting the encrypted response and without decrypting the registration ciphertext. The relationship indicates that equality exists between the first and the second plaintext data sets.