It is enough to modify slightly the way we generate the next jump:
+ jP[tamePosi.x % n]*G if y > p/2, - jP[tamePosi.x % n]*G is y
(then I will indicate 'y' if y > p/2, '-y' if y < p/2)
in this way when a tame T reaches a point Q = (x,y) and a wild W reaches a point Q' = -Q = (x,-y), this become a collision
The tame and the wild will go on with 2 specular paths:
Q -> Q + k*G -> Q + k*G -r*G -> ... -> DP
(x,y) (x1,-y1) (x2,y2) (x0, y0)
-Q -> -Q -k*G -> -Q - k*G +r*G -> ... -> DP
(x,-y) (x1,y1) (x2, -y2) (x0, -y0)
until they reach 2 symetric DP, for both of which we know the private key.
I have created a sort of "brownian motion", my kangaroos keep jumping back and forth.
+ jP[tamePosi.x % n]*G if y > p/2, - jP[tamePosi.x % n]*G is y
(then I will indicate 'y' if y > p/2, '-y' if y < p/2)
in this way when a tame T reaches a point Q = (x,y) and a wild W reaches a point Q' = -Q = (x,-y), this become a collision
The tame and the wild will go on with 2 specular paths:
Q -> Q + k*G -> Q + k*G -r*G -> ... -> DP
(x,y) (x1,-y1) (x2,y2) (x0, y0)
-Q -> -Q -k*G -> -Q - k*G +r*G -> ... -> DP
(x,-y) (x1,y1) (x2, -y2) (x0, -y0)
until they reach 2 symetric DP, for both of which we know the private key.
May be a brownian motion can be interesting (having positive and negative jump).
I have created a sort of "brownian motion", my kangaroos keep jumping back and forth.
I'm not sure to fully understand your idea.
You want to add a condition on the y parity to determine the jump ?
You let the starting positions as they are or you translate them ?
