15. The system according to claim 11 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 one of said at least one other entity, receiving a third intermediate value generated by said other entity using said second intermediate value and information private to said other entity; and using said third intermediate value to generate a selection value used to determine said second plurality of choices.
15. The system according to claim 11 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 one of said at least one other entity, receiving a third intermediate value generated by said other entity using said second intermediate value and information private to said other entity; and using said third intermediate value to generate a selection value used to determine said second plurality of choices. 20. The system according to claim 15 wherein said cryptographic engine is further configured for applying the inverse of said random value to said third intermediate value to derive a third point and rendering said third point to generate said selection value.