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Solve Juggle Pieces

Hello guys, Today is quite interesting topic "Juggle the pieces", this is elaborate after affine ciphers.

Affine Ciphers are monoalphabetic ciphers, because every alphabet map against a number. Affine cipher introduce modulus operator. There are so many ciphers build on affine ciphers. Previous cipher Oh yeah, very well Atbash cipher also a good example of this category.
Mathematical Statement:
                E(X) = D(E(X))-----------------------------------------------------(0)
                here E is a function that take parameter x and return encrypted text. Similar with D function but this is inverse function of E.
                 E(x) = (ax+b) mod m--------------------------------------------(1)
                  a, b are keys and m is size of alphabetic, while modules (mod) is an operator which help to solve the equation. a , m both of them are co prime. X key-factor{R{0,..... m-1}}
                D(x) = a^-1 (x-b) mod m----------------------------------------(2)
 If inverse of a doesn't exit then you can't solve through affine cipher. It's a only condition that is necessary for this type of ciphers.
                   1 = aa^-1 mod m --------------------------------------------- (3)
Equation 3 prove that if a , m are co prime and a doesn't have any restriction it's solvable.

Rail Fence Cipher
Now you can solve monoalphabetic ciphers because you know game rules.
Now time to play with pieces.
This cipher belong to another class of cipher transposition cipher, this cipher called zig zag or rail fence cipher.
  There is a man who had receive a call from a private and he say "HOENEL MSEGRL SE" and then call had ended. He think that is just a prank call but the scene is quit awkward, so he try to decrypt the message will you help him. You can send me answer of this puzzle.
                      message : "All is well"
                     A        L          S        E        L
                          L            I       W        L
                      Cipher text:  ALSELLIWL
How can I write like this, it's simple. In this cipher you can write text in zigzag form. Start from first row, then second row then first and so on. This is the case when key should be 2.
 However if K should be 3 or 4 or any higher order.
              A            S        W            X

                 L         I              E       L

                      L                       L 

Cipher text :      ASWLIELLL
One that i skip X means termination of string.
Thank you for reading


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