Privacy-preserving computation method and system for secure three-party linear regression

A privacy-preserving computation system for secure three-party linear regression, comprising:

• a first private transposed matrix computing module configured to allow a first participant to compute a transposed matrix of a first private matrix to obtain a first private transposed matrix, wherein the first private matrix is a private matrix of the first participant;
• a second private transposed matrix computing module configured to allow a second participant to compute a transposed matrix of a second private matrix to obtain a second private transposed matrix, wherein the second private matrix is a private matrix of the second participant;
• a secure two-party matrix hybrid multiplication protocol (2PHMP) module configured to allow the first participant and the second participant to process the first private transposed matrix, the second private transposed matrix, the first private matrix, and the second private matrix by using a secure two-party matrix hybrid multiplication protocol, to obtain a matrix σ1 and a matrix σ2, wherein the matrix σ1 is stored in the first participant, and the matrix σ2 is stored in the second participant;
• a secure two-party matrix inversion protocol (2PIP) module configured to allow the first participant and the second participant to process the matrix σ1 and the matrix σ2 by using a secure two-party matrix inversion protocol, to obtain a matrix u1 and a matrix u2, wherein the matrix u1 is stored in the first participant, and the matrix u2 is stored in the second participant;
• a splitting module configured to allow the first participant to split the first private transposed matrix into a random matrix v1 and a difference matrix Δ, and send the difference matrix Δ to the second participant;
• an obfuscation and overlay computation module configured to allow the second participant to secretly obfuscate and overlay the second private transposed matrix with the difference matrix Δ to obtain a random matrix v2;
• and
• a secure three-party matrix hybrid multiplication protocol (3PHMP) module configured to allow a requester of secure three-party linear regression computation, the first participant, the second participant, and a third participant to process a first private matrix sequence, a second private matrix sequence, and a third private matrix by using a secure three-party matrix hybrid multiplication protocol, to obtain a regression coefficient matrix of a secure three-party linear regression model, wherein the third private matrix is a private matrix of the third participant, the first private matrix sequence comprises the matrix u1 and the random matrix v1, and the second private matrix sequence comprises the matrix u2 and the random matrix v2.