Public Knowledge

, ,; plaintext alphabet,;

abstract free group, with abstract letters;

set; linear congruence generator h of maximal periodic length.

Alice

Bob

Private keys

Explicit set with words in X, Nielsen reduced set,; seed, one-to-one correspondence,.

Encryption

Choose message

with.

Calculate

, obtain.

Encryption procedure:

if then,

Ciphertext:

with written as words in X.

Decryption

Compute z automorphism:

, obtain.

Two possibilities:

1. For each, compute

and get a table like Table 8 (page 82). (Decryption: Search in this table.)

if then,

2. Use Nielsen reduced set U and an algorithm to write the ciphertext units (given as words in X) as words in U. Together with the used automorphism, the ciphertext is decrypted correctly.

Reconstruct plaintext message

with.