# Is this good way of Elliptical curve point mapping

Mapping a bit string $$L$$ to elliptical curve point in say prime field $$\mathbb Z_p$$. A simple way would be to use an integer mapping function that maps $$L$$ to a number $$\{1, q\}$$ where $$q$$ is the order of the group and then return $$q[B]$$, where $$B$$ is a base point. But it would be unacceptable for the purpose I want.

Here is my design for some mental poker or any card game "https://crypto.stackexchange.com/questions/87159/a-card-game-for-mental-poker-or-any-other-card-game" as it should not allow anyone to compute the discrete logarithm of one point base on another point in the group. So we use a function which maps $$L$$ to a number $$\{1,p\}$$ call it $$x$$ and a bit $$b$$. If any point $$P = (x,y)$$ exists on the curve, return $$[h]P'^*$$ where $$h$$ is the cofactor of the curve and $$P' = (x,y)$$ if $$b=0$$ $$(x,-y)$$ otherwise $$(x,y)$$. Otherwise set $$L = H_{0,..|L|}(L)$$ and repeat the process in a loop until you can find a point. It should be secure (Infeasible to calculate the Elliptical curve discrete logarithm of one point over another as long as the curve is good enough) right?

• – kelalaka Dec 28 '20 at 11:44
• Thank you for this. I would have preferred non reversible but I can simply use a hash function before doing doing this encoding – Manish Adhikari Dec 28 '20 at 12:15