KANGAROO WITH CPU & GPU ACCELERATION TO FIND PRIVATE KEY PUZZLE 145

This program implements a variation of the Kangaroo algorithm (Pollard's Rho for logarithms), a specialized method for solving discrete logarithm problems, adapted for Bitcoin private key discovery. The program aims to find the private key of "Puzzle 145."
Main Components and How It Works:
• Libraries Used:
The kangaroo step uses CPU and GPU for acceleration.
• Kangaroo Algorithm Core:
Tame and Wild Kangaroo: The algorithm conceptually uses two types of "kangaroos" (or points on an elliptic curve): the "tamed kangaroo," which starts from the target public key and jumps backward from a known endpoint, and the "wild kangaroo," which starts from a random point and jumps forward.
pseudo_random_step: Determines the "jump" size for the kangaroo based on its current public key hash.
add_point_scalar: Adds a scalar (a component of the private key) to the public key (a point on the curve), effectively simulating a jump.
Collision Detection: The core idea is that if a tame and a wild kangaroo meet (collide) at the same point, the private key can be derived from the difference between their accumulated steps and their starting point. The program checks for collisions in the tame_filter and wild_filter sets.
Result Handling: If a collision produces a valid private key, it is verified against the target address, printed to the console, and saved to found145.txt.
In short, both programs aim to find Bitcoin private keys, but bitcoin_bruteforce2.cpp uses a more direct bruteforce (random sampling) approach over a wide range, while kangaroo_145_with_CPU_GPU_accel.cpp implements the more sophisticated Kangaroo algorithm, which can be more efficient for certain types of discrete logarithm problems over a specified range. Both utilize GPU acceleration with OpenCL and multithreading for performance.