The "Jumbled" Cipher

Question

The elusive "Jumbled" cipher has stumped scientists and cryptographers alike...

^{Not really, but it will stump you soon...}

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The Jumbled Cipher is a mysterious text cipher that puts text into an unreadable state, making it appear jumbled. Nobody to this point has been able to decode the messy ASCII cipher into its original format.

Here are some examples, showing an example of the algorithm at work:

hello world                 =>      ĄûĎĎđPĥđĚĎú
Puzzling Stack Exchange     =>      ÈģĮĮĎąĐýPËĢñóćP«ĬóĄñĐýû
sp00ky scary                =>      ěĘxxćĭPěóñĚĭ

Your job is to crack the code. You need to figure out what the algorithm is that is being used to encode the string. Your hints follow (more will be added every day the question is not solved).

Hint 1

Take what you will from this riddle: Rumors of an all-smart man were passed around, however, I knew this man, and he was only a bit wise - the rumors were just not true.

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As an extra challenge (optional), you can create an encoder and decoder in the programming language of your choice. It may be featured in this post. Good luck cracking the code!

Answer 1

In each string,

a character with ASCII code c is replaced by one with Unicode code point computed as follows: add together c and floor(c/2), and then subtract 1 if c is odd and another 3 if c has bit 1 set. (That is: write c in binary: if it ends 00, 01, 10, 11 then subtract 0, 1, 3, 4 respectively.)

It feels as if there should be a more elegant way to describe this. Ah, here's one:

compute 2.5*c and then subtract 1.5*(c&3) where the & is bitwise.

Here's another equivalent description:

character c is replaced with c + 1.5*c' where c' = c-(c&3) -- i.e., c' is c with its two low bits cleared. (Which can therefore be multiplied by 1.5 safe in the knowledge that the result is an integer.)

Presumably

the input doesn't have to be within the ASCII range, but of course for some inputs there might not be a Unicode character with the prescribed number...

Solving process:

I looked at the plaintext/ciphertext pairs given and noticed that it seems to be a simple substitution cipher. The first thing that jumped out at me was the 0->x pair, not least because I think it's the only one where the ciphertext is within the ASCII range. 0 is 48 and x is 120, which is ... suggestive. So then I tried mapping c to 2.5*c, rounded one way or another, and noticed that the results were close but wrong. Next thing was to look at the differences. Hmm, they're all (1) small and (2) negative. So which numbers yield which differences? Ah, looks like it only depends on c mod 4. From there it's just a matter of looking for not-too-horrible equivalen ways to describe the calculation.