What would a trapdoor value be for SHA1 ?
What I can agree is that I would like the cryptographic hash to be a one-way function, yes. But not trapdoor functions, please :-)
(and can you point to the definition of the hash functions that you described ? I'm curious).
As for the parenthetical, I'm not sure I take your meaning properly. If you are asking where I learned that hash functions don't have to be one way it seems to be an odd question, but I just checked Wikipedia and it agrees with me, at least.
As for the trivial hash - now I scrolled down the page on Wikipedia, indeed. I never thought of it this way. (That an identity function on an integer would deserve to be called a hash function :-)
The part that got me was the initial sentence about hash function converting "large, possibly variable amount of data" into a "small datum". As "large" and "small" are implied to be of different sizes, I glazed over a possibility of identity function there.
Thanks!