An Improved Non-Iterative Privacy Preservation Lotteries

In 2009, a non-iterative privacy preservation for online lotteries is proposed in IET Information Security by J.S lee, C.S Chan and C.C Chang [1], who claim their scheme achieve the following properties:  Privacy. No one can learn the choices made by lottery players except the players themselves.  Security. No one can counterfeit a winner or forge a winning lottery ticket to claim the prize.  Accuracy. Players can obtain their lottery ticket with preferred numbers.  Anonymity. The lottery ticket can not be linked to the identity of player.  Fairness. Each ticket shall be equally contributed to the winning set.  Convenience. Players need not sophisticated techniques or additional devices.  Public verification. the player shall be able to observe the winning result and verify his lottery ticket.  No online trusted third party needed.  Non-iterative t-out-of-n choice. In Lee-Chan-Chang’s scheme, the main participants include a lottery issuer(LI), a player Alice, an off-line trusted third party(TTP) and a bank(B). Lee-Chan-Chang’s scheme constructs t-out-of-n lottery ticket using the method of robust non-interactive oblivious transfer protocol designed by Yi Mu et al. in 2003[2]. tout-of-n oblivious transfer is defined as follows. Alice knows n messages and wants to send t of them to Bob, Bob gets t of them and knows which ones he has got, but Alice has no idea about which t messages Bob has received. In Lee-Chan-Chang’s scheme, LI knows and publishes n numbers and player Alice gets or selects t of n as his preferred number, then obtains corresponding ticket generated from these t number, LI knows nothing which t number has been chosen. In 2009, some weakness of Mu et al.’s method is analyzed by Chin-Chen Chang and Jung-san Lee [3]. In [3], adversary Bob maybe obtain more than t number through selecting proper public keys ) , ( 1 1 y x , ), , ( 2 2 y x ) , ( , n n y x  determined with