hash functions preimage and second collision resistance A hash function H is secure in terms of pre-image resis-tance. Does this imply that H has second pre-image (aka weak collision) resistance?
No, the implication is wrong.
Pre-image resistance means that it is not possible to calculate a pre-image from the image alone.
But this does not exclude the existence of an algorithm, which calculates a second pre-image, given the image and the first pre-image.