[Cryptography] Name for a specific type of preimage resistance

[Jerry Leichter]

> So I don't think there's a well-established term for that.  The expected
> number of preimages of a "random" function is (if I'm not mistaken)
> e/(e-1) ~ 1.5819767068693, so if a digest is close to "ideal", finding
> any preimage gives you an ~63% chance of finding "the one true"
> preimage, but of course you're concerned with "less than ideal"
> digests...
I'm not sure what this means.  There are (probably) infinitely many pre-images of any given value; in fact, for a "good" function most values must have infinitely many pre-images.  Of course, most of them are very long.

Are you considering the case of a random function from {0,1}^n to itself?  That would be an even more restricted case than the original problem seems to be.

                                                        -- Jerry