Shifting Caesars Shifts

Question

Description

A Caesar Shift is a very simple monoalphabetic cipher where each letter gets replaced by the one after it in the alphabet. Example:

Hello world! -> IFMMP XPSME!

(IBSLR, EGUFV! is the output for the actual challenge, this was an example of shifting by 1.)

As you can see, spacing and punctuation remain unattuned. However, to prevent guessing the message, all letters are capitalized. By shifting the letters back, the message was deciphered, convenient, but also really easy to decipher by other persons who are supposed not to know what the message means.

So, we'll be helping Caesar a bit by using an advanced form of his cipher: the Self-shifting Caesar Shift!

Challenge

Your task is to write a program or function, that, given a string to encipher, outputs the encrypted string corresponding to the input. The advanced Caesar Shift works like this:

1. Compute letter differences of all adjacent letters: 
    1.1. Letter difference is computed like this:

         Position of 2nd letter in the alphabet
        -Position of 1st letter in the alphabet
        =======================================
                              Letter difference

    1.2. Example input: Hello
         H - e|e -  l|l  -  l|l  -  o
         7 - 5|5 - 12|12 - 12|12 - 15 Letter differences: 3; -7; 0; -3
            =3|   =-7|     =0|    =-3
 
2. Assign the letters continously a letter difference from the list,
   starting at the second letter and inverting the differences:
    2.1. 2nd letter: first difference, 3rd letter: second difference, etc.

    2.2. The first letter is assigned a 1.

    2.3. Example input: Hello with differences 3; -7; 0; -3

         Letter || Value
         =======||======
            H   ||   1
            E   ||  -3
            L   ||   7
            L   ||   0
            O   ||   3

3. Shift the letters by the value x they have been assigned:
    3.1. In case of a positive x, the letter is shifted x letters to the right.
    3.2. In case of a negative x, the letter is shifted |x| letters to the left.
    3.3. In case of x = 0, the letter is not shifted.

    3.4. If the shift would surpass the limits of the alphabet, it gets wrapped around
         Example: Y + Shift of 2 --> A

    3.5. Example input: See the table under 2.3.

                ||       || Shifted
         Letter || Value || Letter
         =======||=======||=========
            H   ||   1   ||    I
            E   ||  -3   ||    B     Program output:
            L   ||   7   ||    S     IBSLR
            L   ||   0   ||    L
            O   ||   3   ||    R

Spaces and other special symbols, such as punctuation are skipped in this process. It is guaranteed that your program will be given a string containing only printable ASCII characters. The output of your function/program must only be in upper case.

This is code-golf, so standard loopholes apply, and may the shortest answer in bytes win!

Answer 1

05AB1E, 28 27 24 bytes

láÇ¥R`XIlvyaiAyk+Aèëy}u?

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Explanation

l                          # convert input to lower case
 á                         # keep only letters
  ǥ                       # compute deltas of character codes
    R`                     # reverse and push separated to stack
      X                    # push 1
       Ilv                 # for each char y in lower case input
          yai              # if y is a letter
             Ayk           # get the index of y in the alphabet
                +          # add the next delta
                 Aè        # index into the alphabet with this
            ëy             # else push y
              }            # end if
            u?             # print as upper case

Answer 2

Python 3, 100 bytes

b=0
for c in map(ord,input().upper()):
 if 64<c<91:b,c=c,(c+c-(b or~-c)-65)%26+65
 print(end=chr(c))

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b keeps track of the last letter’s ASCII code, or is initially zero; the formula c+c-(b or~-x) means a letter with ASCII code c gets shifted by c-b if b is non-zero, and c-(c-1) == +1 if b is zero (for the very first letter).

b will never become zero again, as the string is guaranteed to consist of printable ASCII characters.

Finally, 64<c<91 checks if c is an uppercase ASCII letter, and (…-65)%26+65 wraps everything back into the A-Z range.

ovs saved a byte. Thanks!

Answer 3

05AB1E, 32 30 29 bytes

lDáÇ¥1¸ìUvyaiAX¾èAyk+sè¼ëy}Ju

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Answer 4

ES6 ( Javascript ) , 138 bytes :

s=>((s,a,f)=>((r=i=>s[i]&&(a[i]=String.fromCharCode((2*s[f](i)-(s[f](i-1)||71)-38)%26+64),r(i+1)))(0),a))(s.toUpperCase(),[],"charCodeAt")

http://jsbin.com/manurenasa/edit?console

Answer 5

MATL, 27 bytes

tXkt1Y2mXH)tlwdh+64-lY2w)H(

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I think this is the shortest I can get, but there are lots of different varieties since there is a lot of re-use of 'variables' (there are 3 t (duplication), and 2 w (swap) operations, clipboard H is used, and even then there is still a duplicate 1Y2...). Sadly, I couldn't save bytes with the automatic M clipboard.

Over half of the program is dedicated to making it uppercase and ignoring non-alphabetic characters - just the cipher is no more than 13 bytes (Try it online!)

Answer 6

Perl, 9089

Though non-codegolf languages are rarely competitive, we can go below 100 ;)

@a=split//,<>;say uc(++$a[0]).join'',map{uc chr(2*ord($a[$_+1])-ord($a[$_])+!$_)}0..$#a-1

I've decided to ungolf this:

@a = split//,<>; Takes input from STDIN, stores character list (with newline!) in @a.

say uc(++$a[0]) output uppercase first letter shifted by 1. Turns out you can increment a letter in perl if you use a prefix ++. This is a mutator ofc.

2*ord($a[$_+1])-ord($a[$_])+!$_ We are asked to take character at x, and add the difference + (x-(x-1)). Well that's 2x - (x-1). However: I changed the first letter! So I've got to correct that error, hence +!$_, which will correct for having subtracted one too many at position 0 (only case !$_ is not undef ). We then uc chr to get an uppercase letter from the calculated ASCII value.

map{ ... } $#a-2 - $#a is the position to access the last array element. Since I'm adding one I want $#a-1, but because the newline from input needs ignoring, this is $#a-2.

This is concatenated with the first letter, and we are done :)

Answer 7

Perl 5 -F, 73 77 74 bytes

/\w/&&($_=chr 65+(2*($n=ord uc)-65-($!||-1+ord uc))%26)&($!=$n)for@F;say@F

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Answer 8

PHP, 106 98 bytes

pretty nasty that one ... if just base_convert wasn´t that long (or ctype_alpha) ...
but I got it under 100. satisfied.

for(;$a=ord($c=$argn[$i++]);print ctype_alpha($c)?chr(65+($p?(25-$p+2*$p=$a)%26:$p=$a)):$c)$a&=31;

Run as pipe with -nR or try it online.

Answer 9

JavaScript (Node.js), 86 83 87 81 bytes

s=>s.replace(/[a-z]/gi,(x,i)=>Buffer(x).map(x=>((i?x%32-l:1)+26+(l=x%32))%26+64))

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