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A birthday attack is a cryptanalytic technique. Birthday attacks can be used to find collisions in a cryptographic hash function. For instance, suppose we have a hash function which, when supplied with a random input, returns one of $k$ equally likely values. By repeatedly evaluating the function on $1.2\sqrt{k}$ different inputs, it is likely we will find some pair of inputs that produce the same output (a collision).

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Birthday Attack

Here's yet another similar way to get this approximation. Consider every pairing of n elements from H, ignoring elements paired with themselves but not requiring that the elements be unique. i.e. $Le …
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