A garbled circuit and two garbled inputs are received by a server from each pair of a plurality of clients. The garbled circuit encodes a comparison function and the garbled inputs encode a respective data value from each of the clients in each pair. Thereafter, the server evaluates the garbled circuits using the corresponding garbled inputs to result in a plurality of comparison bits. The server can then sort the datasets in an ascending or descending order by using the comparison bits to compute the rank of each data value. Using the sorted datasets, the server determines a median value for the datasets and transmits data characterizing the median value to each of the clients.

A method of manufacturing a secure computing hardware apparatus includes receiving at least a secret generator, wherein the secret generator is configured to generate a module-specific secret, receiving a device identifier, wherein the device identifier is configured to produce at least an output comprising a secure proof of the module-specific secret, and communicatively connecting the device identifier to the secret generator.

System and method of creating a multi-party computation (MPC) cryptographic signature for a blockchain based computer network, including: generating at least one first share and second share of a cryptographic key, based on a distributed key generation MPC protocol, signing a received message with the at least one first share, receiving the message signed with the at least one first share, signing the message signed with the at least one first share with the at least one second share, sending the message signed with the at least one second share and the at least one first share to a full node of the computer network, and adding a transaction to a ledger of the computer network, in accordance with the received message signed by the at least one first share and the at least one second share.

One or more embodiments of the present specification provide privacy protection-based multicollinearity detection methods, apparatuses, and systems. Data alignment is performed by a member device on respective local feature data with other member devices to construct a joint feature matrix. Privacy protection-based multi-party matrix multiplication computation is performed to compute a product matrix of a transposed matrix of the joint feature matrix and the joint feature matrix. An inverse matrix of the product matrix is determined based on respective submatrices of the product matrix. A variance inflation factor of each attribute feature is determined by the member device with the other member devices using respective submatrices of the inverse matrix and the respective local feature data. Multicollinearity is determined by the member device with the other member devices based on fragment data of the variance inflation factor of each attribute feature.

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 generate chronological sequences of encrypted impression data and encrypted conversion data and to decrypt the encrypted impression data and the encrypted conversion data.

A method for privacy-preserving inventory matching may include: (1) receiving a plurality of axe submissions; (2) arranging the parties into data structures based on a direction in the party's axe submission; (3) sending each party's commitment to the other party; (4) receiving, from each party, output secret-shares of an arithmetized comparison circuit; (5) verifying that the output secret-shares of the arithmetized comparison circuit received from the parties match commitments to the output secret-shares sent by the respective opposite party; (6) identifying a minimal party based on the outputs of the arithmetized comparison circuit; (7) generating and sending a proof of the minimal party identification to the minimal party; (8) receiving a minimal quantity integer from the minimal party; (9) revealing the minimal quantity integer to the first party and the second party; and (10) executing the trade for the minimal quantity integer.

A method, in particular, a computer-implemented method, for managing data associated with a product pool including at least two technical products, in particular, machines or vehicles, using a multiparty computation (MPC) process. The method includes the following steps: receiving first input data at at least one first MPC node, the first input data including operating data of the at least one first product, and receiving second input data at an at least one second MPC node, the second input data including operating data of the at least one second product, receiving further input data at one further MPC node, the further input data including the data associated with the product pool, calculating a distribution function based on the first input data, on the second input data and on the further input data, and outputting the distribution function.

A device participates in a cyclical collaboration system. The device receives a request from a third party. A request value is determined that is associated with the request. A first random number is determined based on the first request value. The first random number is provided to a downstream device. A second random number is received that is generated by a upstream device. A first encrypted request value is determined based on the first request value, the first random number, and the second random number. The first encrypted request value is provided to a multiple party encryption subsystem. Encrypted request values generated by other participants of the cyclical collaboration network are received from the multiple party encryption subsystem. A validation score is determined based on the first encrypted request values and the encrypted request values received from the multiple party encryption subsystem.

The present invention relates to a method of secure generation by a client device and a server device of an RSA signature of a message to be signed with a private exponent component d of an RSA key (p, q, N, d, e), wherein said client device stores a client device private exponent component dA, a client value, and a client dynamic offset, and said server device stores a server device private exponent component dB, where dB=d−dA modulo phi(N), a server value, a server dynamic offset and a failure counter, comprising: a. receiving from the client device a client part of said RSA signature (HS1) of said message to be signed, after incrementing its client value (pvA) by a first predetermined step E, from the client device private exponent component and from an updated client dynamic offset function of said client dynamic offset and of said client value, b. setting said failure counter to a first default value, c. incrementing said server value (pvB) by a second predetermined step (E′), d. generating a server part of said RSA signature (HS2) of said message to be signed, from the server device private exponent component and from an updated server dynamic offset function of said server dynamic offset and of said server value, e. generating said RSA signature by combining said client part of said RSA signature (HS1) and said server part of said RSA signature (HS2), f. checking if the generation of the RSA signature was a failure and when it was a failure, incrementing said failure counter and g\ iteratively repeating above steps c\ to f\, until said RSA signature is successfully generated or said failure counter reaches a first predetermined threshold S.

A secure multi-party computation implements real number arithmetic using modular integer representation on the backend. As part of the implementation, a secret shared value jointly stored by multiple parties in a first modular representation is cast into a second modular representation having a larger most significant bit. The parties use a secret shared masking value in the first representation, the range of which is divided into two halves, to mask and reveal a sum of the secret shared value and the secret shared masking value. The parties use a secret shared bit that identifies the half of the range that contains the masking value, along with the sum to collaboratively construct a set of secret shares representing the secret shared value in the second modular format. In contrast with previous work, the disclosed solution eliminates a non-zero probability of error without sacrificing efficiency or security.