need a kangaroo that will receive a public key and compare it with each jump. don't need tables, DP, etc.
what you described it isn't kangaroo it i just regular cracking search and it doesn't have the square root of N benefit of birthday paradox.
You need tables full of DP to make it more efficient and to be able to use the square root of N that bring the Kangaroo algorithm by the birthday paradox.