A first computing device transfers first and second commitments to a second computing device. The first commitment is for private data and a first random number and the second commitment is for second and third random numbers. The method includes producing a result by evaluating a predicate and a first support function of a garbled circuit. The result includes a first part and a second part, referred to as the predicate result. The method includes transferring the result to the second computing device; receiving a second challenge from the second computing device; and producing a second response from a second support function using the second challenge. The method includes transferring the second response to the second computing device. The predicate result over the private data is true if a result of a check function is equal to a third commitment of the first part and the second response.