Yes, I had an ulterior motive in starting this topic right this moment. See, I'm trying to close the inferential gap in explaining Bitcoin to the layperson, so I wrote up a blog post explaining the relevant cryptographic pre-requisites. (It's based on discussions with an economist who plans to write about Bitcoin soon.)

I would appreciate any corrections. Also, this is another case of me claiming to be better at explaining stuff than most people, so see if I live up to the standard (preferably from those that don't already understand this stuff). The economist I talked to found my explanation must more helpful than Wikipedia (and I, too, found the site's explanations not very helpful in my self-education about cryptography).

(Edited to fix typo)

Edit2: Now my long-time frenemy and economist Bob Murphy links the post with approval, though yes, he doesn't specify that it's more of a "cover of the pre-requisites" than an explanation of Bitcoin itself.