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Cubic cipher. key generation. First, form a Keystring like Playfair E.g. Keyword=COLUMBIA Keystring=COLUMBIADEFGHJKNPQRSTVWXYZ. key generation. Then wrap keystring around a 3X3X3 cube, but leave center empty. 2D and 3D views: z=0 z=1 z=2 COL EFG QRS UMB H J TVW IAD KNP XYZ.

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Presentation Transcript
key generation
key generation

First, form a Keystring like Playfair

E.g. Keyword=COLUMBIA

Keystring=COLUMBIADEFGHJKNPQRSTVWXYZ

key generation3
key generation
  • Then wrap keystring around a 3X3X3 cube, but leave center empty.
  • 2D and 3D views:

z=0 z=1 z=2

COL EFG QRS

UMB H J TVW

IAD KNP XYZ

encryption
encryption
  • Basic idea: for a cleartext letter, ciphertext = pair of letters around it on a straight line
  • E.g. FEG and VRY

COL EFG QRS

UMB H J TVW

IAD KNP XYZ

  • Since there’re multiple adjacent pairs, there’re multiple ways to encrypt.
encryption5
Encryption
  • Adjacent pairs can go beyond the cube and “wrap back” to it (or think of the cube as being surrounded by copies of itself)
  • E.g. CLO is also a valid encryption

LCOL EFG QRS

UMB H J TVW

IAD KNP XYZ

encryption6
encryption
  • Two other examples:

CIU CDM

encryption7
encryption
  • A less intuitive example: CPV

COL EFG QRS

UMB H J TVW

IAD KNP XYZ

encryption8
encryption
  • 13 such symmetric pairs (above/below, left/right, in front/behind, in front-above/behind-below, …)
  • Mathematically… (x, y, z = coordinates of letter)

1. x+1 and x-1

2. y+1 and y-1

3. z+1 and z-1

4. x+1, y-1 and x-1, y+1

5. x+1, y+1 and x-1, y-1

6. x+1, z-1 and x-1, z+1

7. x+1, z+1 and x-1, z-1

8. y+1, z-1 and y-1, z+1

9. y+1, z+1 and y-1, z-1

10. x+1, y+1, z+1 and x-1, y-1, z-1

11. x+1, y+1, z-1 and x-1, y-1, z+1

12. x+1, y-1, z+1 and x-1, y+1, z-1

13. x+1, y-1, z-1 and x-1, y+1, z+1

encryption9
encryption
  • Each pair has two directions
  • E.g. COL or LO
  • So, total of 13X2 = 26 pairs
encryption10
Encryption
  • But 2 of them involve the empty space in the middle, so drop them.
  • Overall, 24 possible encryptions for each letter.
encryption11
encryption
  • Which of the 24 encryptions to pick?
  • Use a distribution function to decide
  • Right now, distribution function simply returns random integer from 0 to 24

All 24 encryptions have equal chance

  • More on this later.
decryption
decryption
  • Basic idea: take the two ciphertext characters, find the letter that forms a straight line with them.
  • Technical term? Zeph: “It’s called Cubic projection… or something like that.”
  • Very simple, but not sure how to describe in English.
decryption13
decryption
  • Use 2D as example. Only 2 possibilities
  • Case 1: lie on the same x-coordinate
  • That means cleartext lies on the same coordinate also
decryption14
decryption
  • Case 2: lie on different x-coordinates
  • That means cleartext lies on the third, unoccupied x-coordinate
decryption15
decryption
  • For our case, basically repeat the above for all 3 planes (xy, xz, yz) of the cube
nulls
nulls
  • Nulls = meaningless characters in the ciphertext to confuse cryptanalyst
  • In my cipher, you can produce nulls by encrypting the empty space in the middle
nulls17
nulls
  • E.g. EP/PE and MV/VM are adjacent pairs of the empty space.

COL EFG QRS COL EFG QRS

UMB H J TVW UMB H J TVW

IAD KNP XYZ IAD KNP XYZ

  • So, when decrypted, EP, PE, MV, and VM conveniently become the empty character and disappear: EP’ ‘
nulls18
nulls
  • Some examples:

MVEPVMVMPEVMMVEP

VMMVVMMVOLMVMVMVC

PEEPLOPEEPOLPEEPCC

  • The cipher sprinkles nulls at random throughout the ciphertext
nulls19
nulls
  • (Note: since the adjacent pairs of the empty space cannot contain the empty space itself, all adjacent pairs are valid. So there are 26 possible nulls, not just 24.)
  • (Another note: because of nulls, ciphertext is in general more than twice as long as cleartext)
sample encryptions
Sample encryptions
  • Cleartext:

“If one examines dialectic materialism, one is faced with a choice: either accept textual neocultural theory or conclude that narrative is created by the masses. Many narratives concerning the role of the observer as reader exist.” (From Postmodernism Generator)

  • Ciphertext:

YUNENIQMBITVHESQKOJOHEXFHGFNNZPXZAWYXJQOTVRNQIHEUYTXGELWCXVPBIATRVTRMTXFCFBKNIUXEHOUPVZAQXDVBVNRYXIDNKYWIGTQRACIHMPZGNZDXFOWWYAQUOWGOSSHEHZYANUOBQSDOWYMDJTOEHMLARANMGPDLMQWWLUKWVPSGRKZAULBFBDIYVGYJRSLZIGXLMRWBICWTAHZZDWYVIHEUAXBXUIHGXJCMZCBPSHSWYQFWLPOPLSDMDPVHWIZQIFXMXUOZKAZEPRNGONFMFPYSHWKPVYQEIHZSHRXTSNFLTOKGBIDGBMGSOQXGEUCTJEHHZXUEQGOUTKYKOHSBEHOFNYJYMJMJTPZZRTAVPTJNOZSSBVECIYXUTWHUEDHWKEUSCCXIDAMHETVQLYNQXIBHWSUXRMGMDWLDALSYXGFPXWKBQSPUNQGVRKIIQ

further development
Further development?
  • As I mentioned, right now all 24 (26 for null) ciphers for each letter have equal probability.
  • Dist.Func. just returns random int in [0, 25]

int distFunc(char X) {

return rand.nextInt(26);

}

further development22
Further development?
  • But can make it more complicated by limiting the choices for some letters to less than 24
  • E.g. frequency balancing for homophony
  • Or the opposite: “unbalance” it (make the ciphertext for ‘Z’ the most frequency bigraph) to throw people off (Shane’s suggestion)
further development23
Further development?
  • Encrypt the ciphertext again using the same key or some key derived from it?
  • Instead of adjacent pairs, use weirder pairs (or perhaps determine what to use by looking at the keyword)
weaknesses
Weaknesses
  • subject to bigraph frequency analysis, although nulls and 1-to-24 help a little
  • too simple?
thanks
Thanks!

All Hail the Fu

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