Cryptology - Unofficial St. Mary's College of California Web Site

190 CHAPTER 10. TRANSPOSITION CIPHERS
10.2 Geometrical Ciphers
Traditionally, the most common way of using transposition was to arrange the
plaintext letters in some sort of rectangle. When the insertion and reading of
the letters is done in patterns other than rows and columns, we call the ciphers
Geometrical Ciphers.
Examples: Decipher the geometrical ciphers.
(1) Decipher ANOOR RDXOA OWEOD UNDAN. (Write in 4 rows and read off in a
spiral.)
(2) Decipher IINIZ ATGDZ MTVYY GEERX.
(3) Decipher MOGIN VNNOA IAGLI DAIRC ISTKY. 2
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄
10.3 Turning Grilles
A grille is simply a piece of paper in which holes have been cut. To encipher, lay
the grille on a clean sheet of paper, write your message in the holes, and, once
finished, remove the grill and fill in the leftover spaces with nulls. Deciphering
is easy – lay the grille back on the ciphertext to see the meaningful letters.
Giacolomo Cardano, last seen in Chapter 8.8.4 apparently invented this method
in the 16th century. The problem with this method is that to be secure there
must be many nulls, maybe up to half, and this makes the ciphertext long in
relation to the plaintext. To reduce the number of nulls, we need to be more
careful about where we put the holes. 3
Start with a piece of paper that has a grid marked on it. (A grid here simply
meaning a series of horizontal and vertical lines that visually divides the paper
into equal sized squares.) Select some 2n × 2n collection of these small squares
that forms a large square and divide it into four n × n squares. Fill up the
upper left-hand sub-square with the numbers 1 through n 2 with 1 through n
on the top row, etc.. Then turn your paper one-quarter of the way around and
similarly fill the new upper left-hand square with 1 through n 2 . Repeat this
process twice more, so that each of the numbers is repeated four times in the
big square.
Next, pick exactly one of the four copies of each of the numbers and highlight
or circle it. It’s best if you pick about the same number of numbers from each of
the small squares. Take a new sheet of paper and, using the old as a reference,
2 (1) around and around we go, (2) Read off going down and up the columns: i am
getting very dizzy, (3) Read off the diagonals: moving in a diagonal is tricky.
3 To be precise, the Cardano method actually produces a open cipher rather than a
transposition, but we aren’t that precise.