The analysis of the Kangaroo method does not use the birthday paradox. Close but not exactly. The math behind it is clearly explained in many papers.

But this has nothing to do with address-only puzzles, which are simply brute-force problems. Anything else than this, if proven, automatically implies that secp256k1, SHA, and RIPEMD are all broken, since their cryptographic guarantees would be thrown at the trash.
[/quote]
I'm not referring to the addresses , iam talking about points , how a random jumps give us a collision on the same point after O(sqrt(N))