I’ve been tackling this puzzle named “Hex Cube” from the CSE (Communications Security Establishment, the Canadian “equal” of the NSA) which comes with the directions: “Can you decipher the message? You ought to be capable of in case you return to fundamentals and use slightly little bit of logic.”

Reproduced right here in black and white:

         22 5b 61
         50 76 6d
         77 2a 63
2a 6d 74 70 7c 72 76 76 3f
48 6d 6f 34 77 7a 6a 78 7e
7c 7a 3a 78 78 7e 6f 6a 3a
         77 61 2b
         75 77 58
         6a 76 79
         6a 50 66
         3f 75 68
         6b 75 73

There are 30 completely different hexadecimal symbols on this 54-symbol message, all within the printable character vary of 7-bit ASCII (0x22-0x7f):

      " [ a
      P v m
      w * c
* m t p | r v v ?
H m o 4 w z j x ~
| z : x x ~ o j :
      w a +
      u w X
      j v y
      j P f
      ? u h
      k u s

In response to @JimN’s comment, here is the binary representation:

                           00100010 01011011 01100001
                           01010000 01110110 01101101
                           01110111 00101010 01100011

00101010 01101101 01110100 01110000 01111100 01110010 01110110 01110110 00111111
01001000 01101101 01101111 00110100 01110111 01111010 01101010 01111000 01111110
01111100 01111010 00111010 01111000 01111000 01111110 01101111 01101010 00111010

                           01110111 01100001 00101011
                           01110101 01110111 01011000
                           01101010 01110110 01111001

                           01101010 01010000 01100110
                           00111111 01110101 01101000
                           01101011 01110101 01110011

This is a Rubik’s Cube which can be solved using an online tool in 20 rotations:

R2 U F' U B2 R F' U' D2 R' U L2 U2 D' B2 R2 U' R2 F2 R2

Solved cube:

Shown here in black and white:

         6a 50 63
         7a 76 50
         22 6a 79
7c 6a 6b 2a 58 66 7a 76 72
76 6d 34 6f 77 2a 7c 78 7a
70 75 6f 2b 68 61 73 48 3a
         7e 7e 3f
         5b 77 3f
         74 61 77
         77 78 78
         6d 75 75
         6a 6d 76

And the corresponding ASCII characters are:

      j P c
      z v P
      " j y
| j k * X f z v r
v m 4 o w * | x z
p u o + h a s H :
      ~ ~ ?
      [ w ?
      t a w
      w x x
      m u u
      j m v

And the binary representation:

                           01101010 01010000 01100011
                           01111010 01110110 01010000
                           00100010 01101010 01111001
                           
01111100 01101010 01101011 00101010 01011000 01100110 01111010 01110110 01110010
01110110 01101101 00110100 01101111 01110111 00101010 01111100 01111000 01111010
01110000 01110101 01101111 00101011 01101000 01100001 01110011 01001000 00111010

                           01111110 01111110 00111111
                           01011011 01110111 00111111
                           01110100 01100001 01110111
                           
                           01110111 01111000 01111000
                           01101101 01110101 01110101
                           01101010 01101101 01110110

I figure “back to basics” could refer to “transposition and substitution”. Solving the cube would be the transposition part. For the substitution part, I’m thinking “a bit of logic” could mean some bitwise operation.

That’s where I’m stuck. I’ve tried a number of things (e.g. frequency analysis, ASCII shift) to no avail and could use a hint, if anyone has an idea on how to solve this!

2021-04-18 UPDATE: I wonder if there could be a relation between the rotation of the cubelets from the initial to the solved position and some “bit of logic” (bitwise) operations. The cubelet rotations of the solved cube are show below, where: 0: no rotation; 1: 90° rotation; -1: -90° rotation; and 2: 180° rotation.

          0  1 -1
          2  0  1
         -1  0  0
         
 1 -1  2  0 -1  0   2  2  0
-1  0  2  2  0 -1  -1  0 -1
-1  0 -1  2  1 -1   1 -1  0

          2 -1  0
         -1  0  2
          2  2  2
          
          1  2  2
          2  0  2
          0  2  2       

UPDATE 2021-10-15: Thanks to @fljx for pointing out in the comments that there was a typo in the transcription of the original (scrambled) cube. 6th line, 7th number (yellow of the YRG corner) was incorrectly shown to be 3f – “?”. It is now fixed to show 6f – “o” – 01101111.

Also, following @bobble’s suggestion, I added this puzzle to the list of bounties with no deadlines, whereby a 600-reputation bounty is offered to anyone who can supply an important hint that allows solving this puzzle.

UPDATE 2021-12-27: I wonder, could the 24-bit RGB color codes, or perhaps 8-bit RGB color codes, be involved in some bitwise operation?

        24-bit  8-bit
RED     FF0000 11100000
GREEN   00FF00 00011100
BLUE    0000FF 00000011
YELLOW  FFFF00 11111100
ORANGE  FF8C00 11101100
WHITE   FFFFFF 11111111

UPDATE 2021-12-28: Here is a French version of this same puzzle. Of the 54 hex symbols, there are 36 different symbols, most within the printable 7-bit ASCII interval, except for 0x7f (DEL) and 6 printable symbols in the extended 8-bit ASCII range, most certainly to account for accented letters in the plaintext.

Also, notice the slight difference in RGB code for the white (gray) squares:

        24-bit  8-bit
WHITE   C0C0C0 10110110

The conversion from 24-bit RGB to 8-bit RGB was done using this formula:

8bit Color = (Red * 7 / 255) << 5 + (Green * 7 / 255) << 2 + (Blue * 3 / 255)