asciilifeform: this has ~nothing to do with provably placing transform's inversion into a complexity class.
asciilifeform: i recall there was thread where mircea_popescu suggested the use of nonstandard bases to frustrate enemy per 'specificity of diddling' principle.
asciilifeform: got the ENTIRELY unsurprising 'what, you're a martian?' stare back.
asciilifeform: btw when i went down into the snakepit with several dozen renowned 'cryptographers' earlier this year, i asked a few folks about this.☟︎
asciilifeform: that's the basic boojum of crypto as practiced by extant 'cryptographers'.
asciilifeform: sure. but my inability to do so says NOTHING about its hardness. only about how MY PARTICULAR hands grow out from my arse.
asciilifeform: 'aes is hard to break' 'says who' 'says me, i haven't broken it yet'☟︎
asciilifeform: it is 100% exactly the same case as in symmetric cipherdom.
asciilifeform: and point of thread was 'no one has shown with any degree of rigour whatsoever, ~how~ hard'☟︎
asciilifeform: whole notion of hash is that 'do the inverse' is hard.
asciilifeform: (in the sense that K possible bitstrings could end up at the given nextprime())
asciilifeform: a clearer approach would be to state this in terms of how many bits of entropy, such that is used in generating key, are de facto discarded by the nextprime() op.
asciilifeform: take legendre's approximation, or chebyshev's, and see.