Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In cryptography, a collision attack on a cryptographic hash tries to find two arbitrary inputs that will produce the same hash value, i.e. a hash collision. In contrast to a preimage attack, neither the hash value nor one of the inputs is specified.Mathematically stated, a collision attack finds two different messages m1 and m2, such that hash(m1) = hash(m2). In a classical collision attack, the attacker has no control over the content of either message, but they are arbitrarily chosen by the algorithm.Much like symmetric-key ciphers are vulnerable to brute force attacks, every cryptographic hash function is inherently vulnerable to collisions using a birthday attack. Due to the birthday problem, these attacks are much faster than a brute force would be. A hash of n bits can be broken in 2n / 2 time (evaluations of the hash function).

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