I wanted to understand how the SHA0 hash function was violated. I understand that using hash problems / the principle of holding pigeons, hash collisions were found. http://www.mail-archive.com/cryptography%40metzdowd.com/msg02554.html contains an example message.
I'm having trouble finding / understanding: Does this mean that there is a timely, mathematical way to ALWAYS produce a hash collision?
Can I find m2 for a given m1, so that m1! = M2, sha (m1) == sha (m2), or is it possible only on a subset of the possible messages? Paraphrased: Is it likely that my password will receive another message per collision?
What is the meaning of searching for 2 random long messages, for example, in the link above that have the same hash value? Why should they sift through long random messages for a collision instead of calculating a collision for a practical message such as a “brown dog jumped over a fox”?
A few examples of hash collisions do not seem as important as the timely collision generation method for any message , but all messages speak of the first.
Thanks for any help / your time! I read a lot of posts / articles, but can't work on my confusion. I suspect I have the same questions for other broken hash functions like MD5.
EDIT:
The document (explaining the improved collision search method) referenced in the response