Pollard’s Kangaroo is a classical algorithm It’s useful if you’re doing a classical attack on a known range of private keys, but it’s nowhere near as fast as what a quantum computer could theoretically do.

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Pollard's Kangaroo is an algorithm for solving the discrete logarithm problem (or in the Bitcoin case: solving the elliptic curve discrete logarithm problem (ECDLP)) where you already know that the secret scalar you are trying to find is within a certain range.

The time complexity of Pollard's Kangaroo is 

The time complexity of a naive brute force search is 

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Quantum computing firm offers $22,500 Bitcoin prize to crack a private key

Pollard's Kangaroo is an algorithm for solving the discrete logarithm problem (or in the Bitcoin case: solving the elliptic curve discrete logarithm problem (ECDLP)) where you already know that the secret scalar you are trying to find is within a certain range.

$$Q = k * G$$
You know $$Q$$ (the public key)
You know $$G$$ (the generator point of secp256k1)
You are trying to find $$k$$ (the private key)

The time complexity of Pollard's Kangaroo is $$O(\sqrt{n})$$
The time complexity of a naive brute force search is $$O(n)$$