collisions on hash functions Why do we say that collision-resistance is a "harder" property than second pre-image for hash functions whereas if you have an attack on the second pre-image then you find a collision ?
Moreover, a collision has a good probability to be found in $O(\sqrt{N})$ where $N$ is the size of the hash function outputs, whereas second pre-image needs $O(N)$ ...
It's harder for the designer to make a hash function collision-resistant than second-preimage-resistant, because it's harder for the adversary to find a second preimage than to find a collision.