Figure Captions

2.   A reversible rule. A reversible rule on states formed by breaking the block of a 2-state automaton into frames. a) shows the operation of the rule on 2-state/cell blocks, and b) shows the operation of the rule on 16-state/cell blocks. Shades of gray are assigned to the states arbitrarily. The frame shifts by 1 to the right at each time step. Periodic boundary conditions are imposed on the block.
3.   Forward and reverse iteration of a toggle rule. The top panel shows how the state of a cell at time t+1 depends on the states in a neighborhood at time t. The bottom panel shows how the state of a cell at time t+1 and the states of cells in a 2r-partial neighborhood at time t determines the outermost cell state at time t under a toggle rule.
4.   A balanced radius-5 toggle rule. The evolution of a balanced radius-5 toggle rule such as used in CA-1.0. The block is 256 bits, and periodic boundary conditions are imposed.
5.   Overview of CA-1.0. The major stages of encryption/decryption of a single block under CA-1.0 are shown. The diffusion phases are labeled D, and the substitution phases are labeled S. Cells which depend only on link information are hatched. The link-encrypted link information enters from the side into the diffusion phase of each subround. The link for a subround is drawn from the top of the link triangle at the previous round.
6.   Chain formation. Blocks can be linked together into chains in the same way that subrounds are linked together in the encryption of a single block. This figure shows how links are passed from one block to the next. The initial link is generated within the encryption apparatus. It is destroyed within the decryption apparatus when decryption of the chain is complete. The bits which appear in the ciphertext stream are indicated by a patterned overbar.

7.   Generation of a permutation from a bit string. Shown are three stages in the generation of the permutation 0123 3201 from the bit string 1110. a) The first two bits lead from the root to the leaf labeled 3. b) The next bit leads to the leaf labeled 2 in the rebalanced tree. c) The last bit leads to the leaf labeled 0 in the tree rebalanced from b). The last element of the permutation follows by necessity.
8.   Block vs. link encryption. This figure shows schematically how link and block encryptions fit together in a subround. A link from a subround is broken into two pieces: a link-block and a link-link. Link encryption is then performed. The link-key encrypted link is then fed into the diffusion phase of the next subround. The output of this block diffusion phase includes the link for the next subround. During link encryption, the block undergoes a substitution phase of encryption. Two permutations are generated from the link, one for the block substitution phase and one for the link substitution phase. The box shows how the information generating these permutations is drawn from the link.

9.   Block difference patterns. The top panel shows the difference pattern for a pair of plaintexts which differ in only 1 position. One of the pair is the 0-plaintext, the other the all-but-0-plaintext. A site which differs between the pair is shown in black, no difference in white. Note that by the second diffusion phase the difference has permeated the entire block. Note further that positions within the link are not changed as the initial link is the same for both members of the pair. The bottom panel shows the decryption of a pair one member of which is the ciphertext for the 0-plaintext, and the other member of the pair is the same ciphertext in which a 1 bit error has been made. By the second substitution phase differences may be found throughout the intermediate ciphertexts.
10.   Rule 30 pairs XOR table with a fixed link. The plaintext pair/ciphertext pair XOR table for rule 30 applied to 4-bit blocks, and iterated 4 times is shown. The link is fixed at 00001110.

11.   Observable rule 30 pairs XOR table. This table is the sum over all tables which can be produced as in figure 10 by changing the link. This is the pairs XOR table which can be actually seen in cryptanalytic experiments.

12.   Link difference patterns. This figure follows the format of figure 9. Here the input block information is fixed between the two runs, and a 1 bit error introduced in the link information, either the link plaintext (top) or the link ciphertext (bottom). Note that manipulation of the link plaintext is not possible in actual use of CA-1.0.