On the Subject of the Binary CM

A machine that knows no bounds when it comes to ciphers.

From the Binary Cipher module by Boxbomb.

Step 1: Axial Symmetry Transposition

Create five 4 by 4 grids by following the steps below:

Grid #1:

Convert the letter on screen A to a Value via the Value Table. Take the resulting value, modulo 8, plus 1. Fill the 1st and 2nd rows with the numbers 1 through 8, with the calculated value at the 1st position, and continuing in reading order.

Convert the letter on screen B to a Value via the Value Table. Take the resulting value, modulo 8, plus 1. Fill the 3rd and 4th rows with the numbers 1 through 8, with the calculated value at the 1st position, and continuing in reading order.

Grid #2:

Convert each hexadecimal character on screen 1 to get a 16-bit binary number. Fill the 4 by 4 grid with these bits.

Grid #3:

Take each cell in Grid #1 in reading order, and compare it to the cell horizontally opposite it in Grid #2. If the numbers are both even or both odd, place a 1 in the cell in Grid #3. Otherwise, place a 0.

Grid #4:

Convert each hexadecimal character on screen 1 to get a 16-bit binary number. Fill the 4 by 4 grid with these bits.

Grid #5:

Take each cell in Grid #3 in reading order, and compare it to the cell horizontally opposite it in Grid #4. If the numbers are both even or both odd, place a 1 in the cell in Grid #5. Otherwise, place a 0.

Hexadecimal to Binary

01234567
00000001001000110100010101100111
89ABCDEF
10001001101010111100110111101111

Example

Screen A Value: 2
Screen B Value: 1
Screen 1: 263E
Screen 2: 2657

Grid #1Grid #2Grid #3Grid #4Grid #5
2345
6781
1234
5678
0101
0000
0010
1101
0000
1010
0001
1110
0110
1111
1001
0100
1001
1010
0111
0011

Step 2: Alphabet Transposition

Create a key using the keyword on screen 3 and the Boolean Expression on screen C. Remove the last 10 letters and rearrange the key into a 4 by 4 grid. Label the columns 1 through 4, left to right. Label the rows 1 through 4, top to bottom. This will be referred to as the Binary Key.

For each letter of the encrypted word, do the following:

  • Identify what table you’re using based on the Nth letter of the encrypted word.
  • Find the Nth letter on screen 4 in the Binary Key.
  • Shift the X marks down equal to the row in the Binary Key.
  • Shift the X marks to the right equal to the column in the Binary Key.
  • Take all the positions of the X marks in reading order and take the binary digits of their positions from Grid #5.
  • Convert the 5-bit binary into a letter via the ASCII Translation Table to get your Nth decrypted letter.

ASCII Translation Table

A00001H01000O01111V10110
B00010I01001P10000W10111
C00011J01010Q10001X11000
D00100K01011R10010Y11001
E00101L01100S10011Z11010
F00110M01101T10100
G00111N01110U10101
ABCDEFGH
X-X-
X---
-X--
--X-
XX--
-X--
-X-X
----
XX--
X-X-
----
--X-
XX--
----
---X
X-X-
XXX-
----
X---
---X
XXX-
-X-X
----
----
XX--
XX--
-X--
----
XX--
X---
-XX-
----
IJKLMNOP
XXX-
----
--XX
----
XX--
---X
--X-
X---
XX--
-X-X
----
--X-
XX--
-X-X
-X--
----
XX--
-X--
X---
--X-
XX--
--X-
--XX
----
XX--
---X
-X--
--X-
XX--
---X
X--X
----
QRSTUVWX
XX--
--XX
----
---X
X-X-
X---
---X
X---
XX--
----
X-X-
--X-
XX--
X--X
----
--X-
XXX-
-X--
----
X---
XX--
--X-
X---
X---
XXXX
X---
----
----
XXX-
----
----
X-X-
YZ
X-X-
X---
-X--
X---
X-X-
-X--
X---
X---

Example

Encrypted Word: LVZG
Screen 4: BTJE

1234
1STAR
2BCDE
3FGHI
4JKLM
1001
1010
0111
0011
--X-
----
-XX-
X-X-
01101 → M
1001
1010
0111
0011
--X-
--XX
X---
--X-
01001 → I
1001
1010
0111
0011
-X-X
--X-
-X--
-X--
01110 → N
1001
1010
0111
0011
-X--
----
XX--
XX--
00100 → D

Decrypted Word: MIND