Systems, methods, and computer-readable media for facilitating an authentication processing service are provided.

A secret share value [q] of a quotient q of a/p is obtained through secure computation using a secret share value [a] and a modulus p and [a/d.sub.0]=[(a+qp)/d.sub.0]?[q]p/d.sub.0, . . . , [a/d.sub.n?1]=[(a+qp)/d.sub.n?1]?[q]p/d.sub.n?1 are obtained and output through secure computation using secret share values [a] and [q], divisors d.sub.0, . . . , d.sub.n?1, and a modulus p. Here, [?] is a secret share value of ?, a is a real number, n is an integer equal to or greater than 2, d.sub.0, . . . , d.sub.n?1 are divisors of real numbers, p is a modulus of a positive integer, and q is a quotient of a positive integer.

A method comprises receiving, from a remote device, a first encrypted data set encrypted using a first encryption scheme, performing a set of computations on the first encrypted data set to generate a first set of encrypted results, encrypting the first set of encrypted results using a second encryption scheme to generate a second set of encrypted results, sending the second set of encrypted results to the remote device, receiving, from the remote device, third set of encrypted results in which the first encryption scheme has been decrypted, and generating a set of decrypted results by applying a decryption algorithm to the third set of encrypted results to decrypt the second encryption scheme.

Methods and systems are disclosed herein for cryptographically secured transfer of an item. In some embodiments, the system may cause generation of multiple key shares of a private key from which a blockchain address on a blockchain is derived. The system may generate a cryptographic representation of a physical item to be transferred from the first user to the second user, the physical item corresponding to the first item. The system may cause a first amount of the first item to be transferred to the blockchain address. The system may obtain a candidate cryptographic representation from the second user. The system may generate, based on the candidate hash matching the hash of the feature vector representing the physical item, a signed message using a partial signature of the second user and another partial signature derived from the third key share.

A system and method for a multi-party computation (MPC) is provided. In implementations, a method includes identifying a blockchain network and a computing device to perform an MPC based on an index; generating an MPC request including a function to be performed by the blockchain network and the computing device, data required for the function, and a verification policy defining a verification protocol to be performed by the blockchain network and the computing device; sending the MPC request to the blockchain network and the computing device; and receiving responses from a representative computing node of the blockchain network and the computing device, wherein each of the responses includes: an output of an MPC protocol performed by the blockchain network and the computing device to jointly compute the function while keeping the inputs private from one another and private from the computing system; and a proof based on the verification policy.

An individual one of secure computation server apparatuses in a secure computation system includes: a local reshare part that computes an arithmetic share from a logic share without communicating with the other secure computation server apparatuses by setting a sub-share not held thereby to zero; a secure computation part that performs a secure computation with communications by using the arithmetic share acquired by the local reshare part, to acquire an arithmetic share from the logic share through a bit conversion; and a comparison and verification part that compares received values with each other, which are received from at least three of the secure computation server apparatuses and which are supposed to be a same value, and adopts the received values that are same at least two received values as an accurate value. The comparison and verification part verifies the received values acquired in the secure computation with communications.

Exemplary embodiments provided herein include a method for safe creation, custody, recovery and management of a digital asset, agnostic to an underlying blockchain technology, the method including establishing a virtual layer where three private keys are generated, transacting the digital asset by using two of three of the private keys and multi-party computation techniques, abstracting interactions between the three private keys from the underlying blockchain technology, having a digital asset transaction considered as a single-signature by the underlying blockchain technology, and recovering the digital asset if any of the three private keys is no longer available. Additionally, the digital asset may be a cryptocurrency, and a party may be disconnected from any network during the normal user operation phases. Furthermore, the digital asset transaction may be considered as a single-signature, as seen by the underlying blockchain technology, and is associated to a public key PK_ABC.

Methods, systems, and apparatus, including a method for determining network measurements. In some aspects, a method includes receiving, by a first aggregation server and from each of multiple client devices, encrypted impression data. A second aggregation server receives, from each of at least a portion of the multiple client devices, encrypted conversion data. The first aggregation server and the second aggregation server perform a multi-party computation process to decrypt the encrypted impression data and the encrypted conversion data. Each portion of decrypted impression data and each portion of decrypted conversion data is sent to a respective reporting system.

A computer-implemented method of transferring control of a digital asset on a blockchain network. The method described in one of the embodiments provides an advantage of enabling easy increase of the number of participants in the signature scheme. The method comprises the steps of distributing a version of cryptographic key, encrypted by means of cryptography system, to a plurality of second participants, wherein a homomorphic property enables derivation of a second public key from a first public key and said version of said cryptographic key. The shares communicated to each a first and/or second participant may be inaccessible to each other said first and/or second participants.

Systems and methods for generating min-increment counting bloom filters to determine count and frequency of device identifiers and attributes in a networking environment are disclosed. The system can maintain a set of data records including device identifiers and attributes associated with device in a network. The system can generate a vector comprising coordinates corresponding to counter registers. The system can identify hash functions to update a counting bloom filter. The system can hash the data records to extract index values pointing to a set of counter registers. The system can increment the positions in the min-increment counting bloom filter corresponding to the minimum values of the counter registers. The system can obtain an aggregated public key comprising a public key. The system can encrypt the counter registers using the aggregated shared key to generate an encrypted vector. The system can transmit the encrypted vector to a networked worker computing device.