Prehistory of Cryptography - A Classical Introduction to Cryptography: Applications for Communications Security - page 8

0 →

1

→

Figure 1.2. Pixel coding for visual cryptography.

whose XOR is 0. Hence we can visually decrypt. As an example, Fig. 1.4 shows a
ciphertext, a key, and what we see from the overlay.

1.1.5 Enigma: Toward Industrial Cryptography

A famous example of an industrial encryption scheme is the Enigma machine which
was used by the Germans during World War II.

We let π be a fixed permutation over the 26-character alphabet with the following

properties:

it has no fixed point (

π ( x ) = x for any x ),

it is an involution (

π ( π ( x )) = x for any x ).

We let S be a set of five permutations over the alphabet. For α ∈ S ,welet α i denote

ρ − i

i i

◦ α ◦ ρ where ρ is the circular rotation over the alphabet by one position ( ρ

thus denotes the circular rotation over the alphabet by i positions). We let be any

involution over the alphabet with the property that it has exactly six fixed points. We
pick

σ

α, β, γ ∈ S pairwise different. We pick a number a .

0 ⊕ 0

−→

≈

0 ⊕ 1

−→ =

−→ =

1 ⊕ 0

−→ ≈

1 ⊕ 1

Figure 1.3. Visual pixel XOR.