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Cryptology – methods and their properties

Written on August 19, 2015 by Manuel Wutte

The word ‘cryptology’ comes from the Greeak and means something like ‘hidden, secret’ and represents a science which deals with the security of information.

Cyptology is divided into two main categories – cryptography and cryptanalysis.

Cryptography is the science of algorithms and methods of encryption, whereas cryptanalysis deals with the security of these methods.

A distinction is made between symmetrical and asymmetrical systems.

At the symmetric system the sender and receiver are using the same key. For establishing a communication the key must be exchanged between sender and the receiver firstly. Thereby, this method is very easy to attack (e.g. by sniffing of the traffic).

In the asymmetrical system, however, different keys are used – there’s a public and a private key. Thus, the problem of the symmetrical procedure is resolved.


Classification of ciphers

A basic distinction is made between monoalphabetic and polyalbhabetic ciphers.


Monoalphabetic ciphers

The procedure for this purpose is called “monoalphabetic substitution” and describes an encryption method in which only a single fixed alphabet is used for the encryption. That means a symbol is always be shown on the same location.

The most famous example is the Caesar cipher. In this method, the letters and characters are chosen from fix predefined letters or groups of characters in plaintext.

By specifying the alphabet to use, these characters are simply replaced by others from this. In simple terms, the starting point character is just replaced by another. Is one of these known, the original letter within the entire text is known!

Monoalphabetische Tabelle

A monoalphabetic encryption could the look like this:

Polyalphabetic ciphers

As polyalphabetic ciphers are called methods in which starting letters or characters are assigned to another letter or character.

Unlike monoalphabetic substitution several different alphabets are used for the characters or the plaintext.

According to this principle works, inter alis, the Vigenère or the Advanced Caesar cipher. The emergence of the Vigenère encryption can be incidentally attributes to the 16th century.


Both cyphering types belong to the exchange and substitution ciphers. Depending on the complexity, these are divided into separate types.


Additive cipher

In order to obtain ciphertext, simply add the code words in the additive cipher.

yi = ai + ( zj * mod(g) )


Multiplikative Chiffre

In contrast to the additive cipher the code words aren’t added at the multiplicative cipher, but as the name suggests, they’re multiplied together.

yi = ai * ( zj * mod(g) )


Product- and chained cipher

In the product cipher the information will be encrypted serveral times with the same key. The chained cipher, however, is encrypted with different keys.


Methods of encryption

Polybius cipher

The Polybius ciphery was applied approximately in the years 200 BC to 120 BC in castles.

In this process the word „HELLO“ could e.g. be received as „23 15 31 31 34“.

The principle behind is relative simple: in those days torches were in the castles successively placed in certain pinnacles of two adjacent towers.

For example, there was a torch at position 2 at the left tower, and at the right one another at position 3.

The recipient of the message was from afar this torch observe positions and decrypt this using the Polybius square as coding of the letter ‘H’.

The Polybius cipher is a monoalphabetic method.

Polybius table

Since there’s only place for 25 characters, was abandoned deliberately to the letter ‘J’.


Beaufort cipher

The Beaufort cipher is named after Sir Francis Beaufort.

If we use

yi = ai + ( zj * mod(g) )   =>   ai = yi – ( zj * mod(g) )

so the sender must add the key and the recipient subtract this.

Beaufort realized that you can add the key in the encryption and decryption when you use the following presentation:

yi = -ai + ( zj * mod(g) )   =>   ai = -yi – ( zj * mod(g) )


In the Beaufort cipher the text to be encrypted is diveded into blocks of five characters. Adequte from the encryption table is then used for each of the five characters.

Above are the letters to be encrypted, on the left side there’s the position within the five blocks.

Beaufort encryption table

In order to demonstrate this practically, the following example will be encrypted by Beaufort.

This is a test to demonstrate the cryptographic method.

This then results in the encrypted text:

Vernam cipher

The Vernam cipher refers to various methods of enryption, which are dating back to Gilbert Vernam.

In 1918 Vernam already reported to a patend, wherin a key bit stream is added to a message.

The security of this process is influenced by several factors.

  • When a (long) natural language word is used as key, the Vernam cipher is merely an extension of the Vigenère cipher, in which the secret key has the same length as the plaintext.By today’s standards such a method is consideres as unsafe!
  • If the key is generated by a cryptographic-secure random  generator, so it security is dependent on that of the random generator.
  • If the generation of the key, however, is based on pure chance, so we also speak of the “One-Time-Pad”. Since Vernam was also involved in the development of the One-Time-Pad, it’s often also referred to as ‘Vernam cipher’.This procedure is considered as perfectly secure.



Although cryptography as well as he steganography have the aim to ensure the confidentiality of information, the differ in their starting points.

In the cryptography, the message itself is encrypted to protect the information. The steganography, however, deals with the concealment of the channel, which is used to communicate.

Both methods can be combined together.



Without cryptology with their knowledge and practices secure comunication and data storage in today’s world would be unthinkable.

Be it starting with the simple password storage up to highly secure transmission of banking data – cryptology makes it possible to protect data against third parties.

However, the subject matter is sometimes in the twilight os the law. Governments would like, if necessary, have the option to decrypt the data, but this would be in contradiction with the basic principles. The most famous example of this would be the NSA.

During my tuition I was able to, inter alia, collect a lot of experience in the field of data transmission and security. Therefore I can say, that this is a very complex topic that is beyond the scope, if I had explained each of the details.

For easier understanding, some of the examples were greatly simplified.

How the cryptographic process itself will continue to be developed in the future is difficult to say, but as it looks like at the moment, probably the most important methods (e.g. RSA…) someday could be decrypted by supercomputers within the polynomial time and thus lose their security.