A method for securely communicating secret values (A[i]) from a plurality of parties to a central entity that requests determination of a global value comprising: within each of the plurality of parties, decomposing a respective secret input value (A,... A) into a respective plurality of share values (A[i,j]) such that the respective plurality of share values, when operated on according to a predetermined mathematical operation, yield back the respective secret input value associated with the respective party; applying the plurality of share values as input values to a first multi-element data and computational structure (601, 650) that computes from the share values a unique calendar value (CAL, R, Z) and, for each share value, determines a unique, repeatable relationship enabling recomputation of the calendar value from the corresponding share value; storing the computed calendar value in a bulletin data structure accessible to an independent auditing entity; and transmitting the respective plurality of share values separately to a respective plurality of nodes, each node thereupon computing a respective node output value (S1, S2,..., SK) by applying the predetermined mathematical operation to the share values it has received from the plurality of the parties and transmitting the respective node output value to the central entity; within the central entity, computing the global value by applying the predetermined mathematical operation to the node output values received from the respective nodes; confirming the correctness of the share values transmitted by any chosen one of the parties by querying the bulletin data structure, such that any one of the parties can be verified by the independent auditing entity and is considered validated if, upon subsequent application of the respective plurality of share values as input values to the multi-element data and computational structure, the same calendar value is obtained as was stored from the bulletin data structure. decomposing a respective secret input value (A,... A) into a respective plurality of share values (A[i,j]) such that the respective plurality of share values, when operated on according to a predetermined mathematical operation, yield back the respective secret input value associated with the respective party; applying the plurality of share values as input values to a first multi-element data and computational structure (601, 650) that computes from the share values a unique calendar value (CAL, R, Z) and, for each share value, determines a unique, repeatable relationship enabling recomputation of the calendar value from the corresponding share value; storing the computed calendar value in a bulletin data structure accessible to an independent auditing entity; and transmitting the respective plurality of share values separately to a respective plurality of nodes, each node thereupon computing a respective node output value (S1, S2,..., SK) by applying the predetermined mathematical operation to the share values it has received from the plurality of the parties and transmitting the respective node output value to the central entity; within the central entity, computing the global value by applying the predetermined mathematical operation to the node output values received from the respective nodes; confirming the correctness of the share values transmitted by any chosen one of the parties by querying the bulletin data structure, such that any one of the parties can be verified by the independent auditing entity and is considered validated if, upon subsequent application of the respective plurality of share values as input values to the multi-element data and computational structure, the same calendar value is obtained as was stored from the bulletin data structure.