A method of providing a distributed scheme for executing a RAM program, without revealing any information regarding the program, the data and the results, according to which the instructions of the program are simulated using SUBLEQ instructions and the execution of the program is divided among a plurality of participating computational resources such as one or more clouds, which do not communicate with each other, while secret sharing all the program's SUBLEQ instructions, to hide their nature of operation and the sequence of operations. Private string matching is secretly performed by comparing strings represented in secret shares, for ensuring the execution of the right instruction sequence. Then arithmetic operations are performed over secret shared bits and branch operations are performed according to the secret shared sign bit of the result.