Privacy-preserving machine learning in the three-server model

A method of performing privacy-preserving machine learning in a three-server model, the method comprising performing by a first training computer of three training computers:

• storing a portion of secret-shared private data from a plurality of data clients, wherein each secret-shared data item of the secret-shared private data is represented by three parts, and wherein the secret-shared private data includes a set of training samples, each having features and an output Y, wherein the three training computers comprise the first training computer, a second training computer, and a third training computer;
• initializing values for a set of weights for a machine learning model, the weights being secret-shared among the three training computers;
• truncating a result of a multiplication of a secret-shared feature and a secret-shared weight as part of training the machine learning model, wherein truncating includes:
• performing preprocessing resulting in a random arithmetic share and a truncated random arithmetic share for the first training computer;
• computing a respective result share minus the random arithmetic share resulting in intermediate shares of an intermediate value;
• revealing the intermediate shares to the second and third training computers, resulting in the three training computers storing the intermediate value and truncating the intermediate value, resulting in a truncated intermediate value;
• and
• computing the respective truncated random arithmetic share plus the truncated intermediate value, resulting in a truncated data item, wherein the truncated data item is secret-shared among the three training computers;
• and
• training, by performing additional multiplications and truncations for secret-shared features of the set of training samples and secret-shared weights, a machine learning model for predicting the outputs Y of the set of training samples.

A method of efficiently performing computations using secret-shared data shared among a plurality of computers, the method comprising performing by a first training computer of three training computers:

• storing a portion of secret-shared private data from a plurality of data clients, wherein each secret-shared data item of the secret-shared private data is represented by three parts, and wherein the secret-shared private data includes a set of training samples, each having features and an output;
• initializing values for a set of weights for a machine learning model, the weights being secret-shared among the three training computers, wherein a first shared tensor X comprises secret-shared features and a second shared tensor Y comprises secret-shared weights;
• determining local shares of elements of an inner product z of locally-stored shares of the first shared tensor X and locally-stored shares of the second shared tensor Y;
• summing local shares of the elements of the inner product z to obtain a local share of the inner product z;
• truncating the local share of the inner product z;
• revealing the truncated local share of the inner product to a third training computer;
• and
• receiving a second truncated local share of the inner product from a second training computer.