An arithmetic apparatus includes an interface and a circuity. The interface is connected to an information processing apparatus that is connected to a client apparatus and that processes data in an encrypted state. The circuitry acquires, from the information processing apparatus, encryption input data or encryption target data encrypted with a first encryption key. The circuitry decrypts the acquired, encryption input data or encryption target data with a first decryption key. Then, the circuitry executes a predetermined arithmetic operation on the decrypted arithmetic operation target data, encrypts data of an arithmetic operation result obtained by the predetermined arithmetic operation with the first encryption to key, and outputs the encrypted data of the arithmetic operation result to the information processing apparatus.

The computation efficiency of distributed secure implementation of the computation of a (sum of) products of values Vi, Wi from different servers on a distributed computing system is improved by generation of coefficients of a first polynomial and second polynomial by a first server. The first polynomial P has all numbers Xi from a first data set on the first server as roots. The second polynomial Q has values Q(Xi)=Vi for the numbers Xi from the first data set. The first device transmits coefficients of the first and second polynomial P, Q to a second server in encrypted form. The second sever computes encrypted values <P(Xi)> and <Q(Xi)> of the first and second polynomial P, Q for a number Xi in a second set from the encrypted coefficients. The second server uses a secure multiparty equality protocol to compute an encrypted binary value <di> from the encrypted value <p(XT) of the first polynomial p, having a first and second binary value when the value p(Xi) of the first polynomial p is zero and not zero respectively. The second server uses a secure multiparty multiplication protocol to compute an encrypted value of a product <di Q(Xi) Wi> and the second server may compute a sum encrypted sum of the products from the encrypted product <di Q(Xi) Wi> computed for all of the numbers Xi and associated values Wi from the second set.

Disclosed herein are methods, systems, and apparatus, including computer programs encoded on computer storage media for secure collaborative computation of a matrix product of a first matrix including private data of a first party and a second matrix including private data of the second party by secret sharing without a trusted initializer. One method includes obtaining a first matrix including private data of the first party; generating a first random matrix; identifying a first sub-matrix and a second sub-matrix of the first random matrix; computing first scrambled private data of the first party based on the first matrix, the first random matrix, the first sub-matrix, and the second sub-matrix; receiving second scrambled private data of the second party; computing a first addend of the matrix product; receiving a second addend of the matrix product; and computing the matrix product by summing the first addend and the second addend.

A method of performing a Multi-Party Computation (MPC) process between two parties and a server, the parties generating initial garbled labels to an initial garbled circuit and sending the initial garbled labels corresponding to an input to the server, the parties generating a fresh garbled circuit and generating multiple bridge gates for translating the initial garbled labels to garbled values for the inputs to the fresh garbled circuit, where each of the bridge gates is associated with a specific input wire of the fresh garbled circuit and maps a value of the initial garbled labels to a value of garbled labels of the fresh garbled circuit, where the server computes fresh garbled values for the fresh garbled circuit using the bridge gates and the initial garbled values and evaluates the fresh garbled circuit using the fresh garbled labels.

An item rating and recommendation platform identifies rating data including respective ratings of multiple items with respect to multiple users; identifies user-feature data including user features contributing to the respective ratings of the multiple items with respect to the multiple users; and receives, from a social network platform via a secret sharing scheme without a trusted initializer, manipulated social network data computed based on social network data and a first number of random variables. The social network data indicate social relationships between any two of the number of users. In the secret sharing scheme without the trust initializer, the social network platform shares with the item rating and recommendation platform manipulated social network data without disclosing the social network data. The item rating and recommendation platform updates the user-feature data based on the rating data and the manipulated social network data.

Disclosed herein are methods, systems, and apparatus, including computer programs encoded on computer storage media, for secure multi-party computation. One of the methods includes identifying a trusted input data item that is homomorphically encrypted; generating a message authentication code (MAC) key share; generating a MAC share associated with the trusted input data item, wherein the MAC share is a random number; generating a ciphertext based on the trusted input data item, the MAC key share, and the MAC share; sending the ciphertext to the second computing device, wherein the second computing device uses the ciphertext as a component of a MAC share associated with the secret input data item; and after the multi-party computation is completed by the plurality of computing devices, verifying a result of the multi-party computation based at least in part on the MAC share associated with the secret input data item.

A method for using biometric data to authenticate a subject as an individual whose biometric data has been previously obtained using a first transducer, the method utilizing computer processes including: generating shards from a digital electronic signal, provided as an output by a second transducer, such signal characterizing a biometric of the subject; causing distribution of the generated shards to an array of servers, so that the array of servers can store the generated shards and perform a data exchange process using a subset of the generated shards to develop information relating to authentication of the subject, where the authentication information includes a key of the subject, and processing the authentication information in a verification process to indicate whether the subject is authenticated as the individual.

Provided herein are systems, devices and methods for transferring cryptocurrency from a limited access cryptocurrency wallet. The limited access cryptocurrency wallet may create, in advance, provisional account(s) allocated for respective recipient(s) and transfer a predefined overall value of cryptocurrency from its associated account associated to the provisional account(s). The limited access cryptocurrency wallet may further generate, in advance, a plurality of signed transactions for transferring a plurality of predefined partial values of cryptocurrency from the provisional account(s) to receiving account(s) associated with the recipient(s) and transmit the plurality of signed transactions to a network connected device. Later, in real-time, the network connected device may transmit one or more of the plurality of signed transactions for transferring cryptocurrency from the provisional account(s) to the receiving account(s) without physically attending to the limited access cryptocurrency wallet.

A method for performing privacy-preserving or secure multi-party computations enables multiple parties to collaborate to produce a shared result while preserving the privacy of input data contributed by individual parties. The method can produce a result with a specified high degree of precision or accuracy in relation to an exactly accurate plaintext (non-privacy-preserving) computation of the result, without unduly burdensome amounts of inter-party communication. The multi-party computations can include a Fourier series approximation of a continuous function or an approximation of a continuous function using trigonometric polynomials, for example, in training a machine learning classifier using secret shared input data. The multi-party computations can include a secret share reduction that transforms an instance of computed secret shared data stored in floating-point representation into an equivalent, equivalently precise, and equivalently secure instance of computed secret shared data having a reduced memory storage requirement.

Disclosed herein are methods, systems, and apparatus, including computer programs encoded on computer storage media, for secure multi-party computation. One of the methods includes identifying a trusted input data item that is homomorphically encrypted; generating a message authentication code (MAC) key share; generating a MAC share associated with the trusted input data item, wherein the MAC share is a random number; generating a ciphertext based on the trusted input data item, the MAC key share, and the MAC share; sending the ciphertext to the second computing device, wherein the second computing device uses the ciphertext as a component of a MAC share associated with the secret input data item; and after the multi-party computation is completed by the plurality of computing devices, verifying a result of the multi-party computation based at least in part on the MAC share associated with the secret input data item.