Temporarily hidden bit commitment and lottery applications

This paper describes various types of commitment functions that maintain a secret for a predictable time delay or until a moderate and predictable amount of computation has occurred. The properties we set out for such functions are based on their usefulness for various applications, such as publicly verifiable lotteries, rather than for cryptologic investigation of the functions. In these lotteries, winners are chosen fairly using only internal information. Since all this information may be published (even before the lottery closes), anyone can do the calculation and therefore verify that the winner was chosen correctly. Since the calculation uses a delaying or similar function, neither ticket purchasers nor the lottery organizer can take advantage of this information. We describe several such lotteries and the security requirements they satisfy, assuming that functions with the properties we state are used.