Regular mono alphabetic substitutions offer little security. Simple frequency distribution analysis will quickly reveal the more common letters, and from there a contact chart will help form common words. A little ingenuity and imagination will allow the cryptanalysist to complete the plaintext…and it's broken.

Variants are one of the simplest ways to help confuse cryptanalysists' attempts at deciphering. The Polybius system (named after the greek who created it) was the first to use numbers to represent letters. The original system did not use variants but simply created a grid, as shown below. To send the plaintext letter 'c', the system would have specified '15' for the ciphertext. The Polybius system is no different than other mono alphabetic systems since every '15' will stand for 'c'. The following example will give you a good understanding of the Polybius system

plaintext:  humor is a universal language - Joel Goodman
plaintext:  h u m o r i s a u n i v e r s a l l a n g u a g e
ciphertext: 23453234422443114533245115424311313111332245112216

With a little reworking, the Polybius systems easily becomes much more powerful than a regular monoalphabetic substitution. By assigning more numbers to the rows and columns, each number can be represented with more than just one number. If the encoder of the message is good, they will use as many variations as allowed for more popular letters and the same ciphertext equivilent of the less common letters. Effective encoding with variants will yield frequency distribution charts far less useful than monoalphabetic substitutions. In the example below, 'to' was encoded 9 different ways (3 options for 't' times 3 options for 'o', 3*3=9). Similarly, 'the' could be encoded 27 different ways.

plaintext:  to   to   to   to   to   to   to   to   to
ciphertext: 4226 4266 4256 7226 7266 7256 9226 9266 9256

For example, the following ciphertexts were created using the Polybius system, one with variants and one without. As you should see, the system using variants has far fewer repetitions of common terms in the regular crypanalysis

plaintext: death is a low chemical trick played on everybody except sequoia trees - J.J. Furnas
ciphertext (polybius w/o variants): 14 15 11 44 23 24 43 11 31 34 52 13 23 15 32 24 13 11 31 44 42 24 13 25 35 31 11 54 15 14 34 33 15 51 15 42 54 12 34 14 54 15 53 13 15 35 44 43 15 41 45 34 24 11 44 42 15 15 43
ciphertext (polybius w/ variants):  14 85 81 43 18 19 41 11 23 26 45 83 18 15 24 19 13 31 23 72 29 19 13 22 27 23 11 97 35 14 26 25 15 44 15 29 77 12 26 14 47 85 46 33 35 27 72 71 85 28 91 11 19 72 29 15 35 41

A second system, called the Playfair, produces a similar effect, which you can learn about next.