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thank you very much hi everybody so this talk about is about how to remove the stronger is the assumption from arguments of are the integers okay thats not what I want and so you know what a commitment scheme here there is a sender that has some message you can lock it into a box and the Box hides a message you cannot see whats inside but at the same time when the sender later revealed a message thats inside the box he cannot change his mind the message so what we will look at today is a commitment skin that has been introduced in 1997 by Fujisaki Nakamoto who which has a nice property which is that it allows to commit to a message M which is over a group of unknown order and this has proven very useful it this commitment scheme was used in a large number of application just to name a few it was useful to build an PC and it was credential e-cash range proof functions password protected secret cheering and so on so the main reason why it enjoyed all those applications is well there a
