Historical Cryptosystems - Everyday Cryptography - page 52

corresponding plaintext letter in the top row. Hence ciphertext IXGGDUM is
decrypted to BUZZARD .

FITTING THE SIMPLE SUBSTITUTION CIPHER TO THE BASIC MODEL
The Simple Substitution Cipher can also be fitted to the basic model of a
cryptosystem of Section 1.4.3. The various components of this model are:

Plaintext/Ciphertext : these are again both defined on the simple alphabet
consisting of the single letters A to Z.
Encryption key : this is the chosen permutation of the letters of the alphabet.
Decryption key : this is the same as the encryption key, so this is a symmetric
cryptosystem.
Keyspace : this is the number of possible permutations of letters of the alphabet
(we discuss this shortly).
Encryption algorithm : this can be represented by the algorithm -

1. write the chosen permutation of letters underneath the naturally ordered
letters of the alphabet;
2. replace the plaintext letter by the ciphertext letter beneath it.

Decryption algorithm : this can be represented by the algorithm -

1. write the chosen permutation of letters underneath the naturally ordered
letters of the alphabet;
2. replace the ciphertext letter by the plaintext letter above it.

KEYSPACE OF THE SIMPLE SUBSTITUTION CIPHER
We have just seen that the key used in the Simple Substitution Cipher is a
permutation of the letters of the alphabet. This means that the size of the keyspace
of the Simple SubstitutionCipher is the number of possible different permutations
of the letters of the alphabet (since each choice of permutation is a possible key),
which we know is 26! So, how big is 26!? Amazingly, 26! is approximately:

10 26 4 × = 400 000 000 000 000 000 000 000 000 .

To obtain an idea of just how big that is, there are an estimated 10 sextillion (that's
10 22 ) stars in our universe. That means that the Simple Substitution Cipher has
about 40000 times more keys than there are stars in our universe.
In Section 4.4 we will discuss the symmetric encryption algorithm DES, which
was the most important symmetric encryption algorithm of the late 20th century.
DES uses keys that are 56 bits long, which means that the size of the keyspace of
DES is 2 56 . By using a useful conversion between powers of 2 and powers of 10
(see Mathematics Appendix) we can see that the size of the keyspace of DES is
somewhere between 10 16 and 10 17 . This is much smaller than the keyspace of the
Simple Substitution Cipher, being 'only' about

1

100 000 of the number of stars in

our universe.