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First of all, "Is collision less likely for individual characters than for strings?" The answer to this is yes. In fact, experimentally verifying shows that for 8-bit ASCII characters the collision chance with FNV1a is 0. This is however not an impressive feat, seeing that the output is 4 times as large as the input. However, using this you no longer have ...

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The answer to your edited question is "yes, it is possible". As a trivial example, let $H$ be an ideal $k$-bit hash function. Due to the existence of the generic birthday attack, $H$ provides only about $k/2$ bits of collision resistance — that is, an attack can, on average, find a collision after about $2^{k/2}$ hash function evaluations. Denote ...

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An asymptotic formalization cares only about what happens when the security parameter becomes "large enough". Since we use (essentially) one fixed security parameter, it is certainly possible to construct cryptosystems that would be insecure for some fixed security parameters, but secure in an asymptotic formalization. This means that a non-asymptotic ...

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