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The quoted text seems to talk about finding a collision of a 128-bit hash function with the Birthday attack. In a birthday attack, one creates around $\sqrt{2^{128}} = 2^{64}$ messages so that they expect to find a colliding pair with 1/2 probability. In the described attack, Oscar wants to create two specific messages that have the same hash value. $x_1$= ...


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No, there's no easier way than to just try brute force. A hash is constructed deliberately in such a way that even two very close inputs can produce two very different hash outputs. That property is known as the avalanche effect. Is it possible to stumble upon a collision of this hash since I know 322 known digits in the middle of the text? Also no, there ...


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