4. The method according to claim 1 wherein said cryptographic operation comprises combining a current selection with all previous selections to generate a first intermediate value, operating on said first intermediate value to generate a second intermediate value, sending said second intermediate value to another entity in said data communication system, receiving a third intermediate value generated by said another entity using said second intermediate value and information private to said another entity; and using said third intermediate value to generate a selection value used to determine said second plurality of choices.
4. The method according to claim 1 wherein said cryptographic operation comprises combining a current selection with all previous selections to generate a first intermediate value, operating on said first intermediate value to generate a second intermediate value, sending said second intermediate value to another entity in said data communication system, receiving a third intermediate value generated by said another entity using said second intermediate value and information private to said another entity; and using said third intermediate value to generate a selection value used to determine said second plurality of choices. 5. The method according to claim 4 comprising converting said first intermediate value into an element of a finite field used in said data communication system and using said element to derive said second intermediate value.