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Baring an improbable tremendous theoretical breakthrough, any odd of any kind of collision among SHA-512 hashes, for any cause except identical input or computing failure, is negligible in practice; we'll thus handle this from a theoretical standpoint. Let $s=512$ be the hash width; $k=1000$ the number of hash iterations; and $q>0$ the number of stored ...

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a Using a moderate number of iterations is a standard approach in password based key derivation (see for example, http://en.wikipedia.org/wiki/PBKDF2, RCF 2898 http://tools.ietf.org/html/rfc2898). It can also be used in the sceanrio described. In this case if an attacker gets access to your password database it should slow down the attacker by a factor ...

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The parameter $k$ appeared in the definitions of hash functions, since many properties are difficult to formulate for a single concrete hash function. For instance, what would it mean that SHA-256 is collision resistant? Clearly, there are values that collide, and there exists a very short algorithm that outputs a collision in a small constant time. To ...

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Security properties of hash functions are generally concerned with collision resistance, but preimage resistance is also important. For most common hash functions with an $n$-bit digest size, a successful preimage attack has generic $2^n$ maximum complexity, and a successful collision attack has generic $2^{n/2}$ maximum complexity. Most common hash ...

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Hashes should work on any number of input bits (almost all I/O parameters in cryptography are defined in bits). The output size for collision resistance should be twice the security level. So for a 128 bit level, use 256 bit hashes.

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