"Two-way hash function" is an oxymoron. The fundamental characteristic of a function that makes it a hash function is the inability to (feasibly) reverse it.
I agree with your final conclusion, that Base64 is an encoding, but it is also a hash function and hash functions can very well be two-way. In fact, the trivial hash function just maps data to itself, which is trivially reversible. However, we do want our cryptographic hash functions to be trapdoors to be of use.
Trapdoor function means the function is easy to calculate in one direction, but is difficult to calculate in the other direction without knowing a special bit of information that allows this calculation much easier.
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).
> What would a trapdoor value be for SHA1 ?
Okay, you got me there. It's been long enough since I've actually used the term that I seemed to have remembered it being the same as one-way. Oops.
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.
"Okay, you got me there." - it was not really intended as a trick - sorry for the wording.
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.
Oh, I didn't think you intended to trick me. Perhaps some context that'd help you understand my state of mind when I wrote that: while I may be a dev and hacker professionally and as a hobby, I went to university in mathematics specialising in number theory. I'm expected to know silly things like the difference between "one way function" and "trapdoor function", so it's a touch off-putting when I forget.
I know what you mean. For me it was: "Hm. he wrote that with a good confidence. Which part of my knowledge is wrong or incomplete ?" :-) Kind of the same feeling when the significant other garbage-collects a pen you put on the table just a few minutes ago.
Base64 is an encoding.