Decision trees can be securely evaluated with reasonable computation speed and bandwidth utilization. A user device encrypts input vectors using a client's public key in an additively homomorphic encryption system. A server computer effectively randomizes the decision tree for each use, such that a value indicative of a path resulting from applying an input vector to the decision tree is different each time the decision tree is used. The server computer homomorphically computes the evaluations of each decision node. The server computer provides the value indicative of the path through the decision tree as one part accessible by the client, and another part accessible by the server. The server computer uses the parts to look up a corresponding output value from a database of output values for each path. In this operation, only the output value corresponding to the combined parts can be retrieved, and only by the intended recipient.