Many encryption methods operate with numbers rather than letters. At the start of the encryption process, a sequence of numbers must therefore be generated from a sequence of letters, the plaintext. This process is also called encoding. Although it may at first sight appear the same, encoding is not yet encryption.

In computers, texts are represented by sequences of numbers between 0 and 255. Those are exactly the numbers that can be expressed by a byte. Nowadays, an encoding called UTF-8 is mostly used. Upper- and lower-case letters are mapped as follows in this system:

The Caesar cipher dates back to Roman general Julius Caesar, who used it to communicate with his troops.

This method worked well in Caesar's day, when almost no one could read and write. Nowadays, however, it is very insecure.

With a substitution cipher, also called monoalphabetic substitution, certain letters are stipulated in a secret key as matching other letters. Each letter of the plaintext is subsequently encrypted using these pre-established letter pairs. The Caesar cipher is a simple example of such a substitution cipher. Another example is the following allocation of letters:

In total, 403,291,461,126,605,635,584,000,000 possible options exist for such letter swaps. That makes it unfeasible to simply try all the possibilities. This encryption was widely used in Europe in the Middle Ages and was considered unbreakable. However, in the Arab world people had known since the ninth century that such methods could be attacked quite easily. The Arabs had realized that not all letters occur in texts with the same frequency. Some letters, such as “E”, are found very frequently, while others, such as “Q”, occur very rarely.

Letter frequencies depend on the language. In German, for example, the distribution looks like this:

That means that counting which letters occur most often in the encrypted text often makes it possible to guess fairly rapidly some of the letter matches used. Once the first few letter correspondences have been established, more can generally be worked out pretty quickly.

There are many strategies to get round the problem of letter frequency. The most important is probably opting not to use the same substitution for every letter.

This can also be described with the encoding mentioned above: to add two letters, for example “M” and “U”, each is written as a number between 0 and 25. “M” becomes 12, “U” becomes 20. Next, those two numbers are added together: 32. If the figure obtained is 26 or higher, subtract 26. That turns 32 into 6. Through the encoding step, that number is expressed as the letter “G”. It is, however, much easier to do this with the above table.

Decryption works along the same lines:

Subtraction is needed for decryption. That is not so straightforward using the tabula recta shown above, but a corresponding table can be set up for subtraction:

Unfortunately, as it turned out, this procedure is not secure either. Mathematician Charles Babbage (1791–1871) and infantry officer Major Friedrich Kasiski (1805–1881) both managed to crack the code independently. Although Babbage found the solution years before Kasiski, he never published it and it was discovered in his estate. These attacks take advantage of the generally short secret text, which often consists of just one word.

In his 1883 text La Cryptographie militaire, Dutch linguist and cryptologist Auguste Kerckhoffs established rules for confidential communication. The most important of these rules is that “the system must not require secrecy.” This rule is often referred to as Kerckhoffs's principle.

Various people came up with the idea of improving the Vigenère cipher by using a secret text that is at least as long as the plaintext. This was first proposed by Frank Miller in 1882. The most important point is to use the key text only once, which is why this method is also called a one-time pad.

One case where this proved devastating was in what is known as the Venona project. During the Second World War and the subsequent Cold War, one-time pads were one of the methods used to protect communications between Soviet embassies and Moscow – but, the key texts were sometimes reused in a slightly altered form. That allowed American and British intelligence services to decipher some of these communications.

For a long time, both encryption and decryption were tedious and time-consuming tasks. That is why mechanical and electrical tools were invented to handle all or part of the encryption and decryption. The most famous is Enigma, which was used by the Germans to encrypt communications before and during the Second World War.

Modern encryption methods use bits rather than the letters of the alphabet. All data in computers is stored as sequences of zeros and ones, known as bits. Encryption methods use a sequence of bits as input data and then obtain a secret key, likewise as a bit-sequence, and use it to calculate the encryption, which is also a sequence of bits. The operations involved can be carried out rapidly by a computer, whereas it would be a very lengthy process if done manually.

Asymmetric encryption methods are a very exciting innovation that would not be feasible in practice without computers. In classical, symmetric methods, both parties must agree on a secret key known only to them. In asymmetric methods, each party has two keys: a secret key that no one else may know and a public key that anyone can know.