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In the context an of hash functions we have three required properties.

  1. Preimage resistance
  2. Second preimage resistance
  3. Collision resistance.

The bounds for Pre image collision is $O(2^{n-1})$, the bounds for collision resistance is $2^{n/2}$, what are the bounds for breaking second preimage resistance?

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The right terminology is second preimage resistance and preimage resistance.

Edited to reflect comment by otus. Preimage attack takes $O(2^{n})$ hash function calls on average.

Second preimage attack takes just one extra call so the complexity is essentially the same as that of the preimage attack. Given $x$ you want $x'\neq x$ such that $H(x)=H(x').$ So evaluate $H(x)$ for one extra query, and then apply the preimage attack to $y=H(x).$

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