Cryptology What is a Cipher?

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The subject of cryptography is the transformation of character strings.

Therefore in parallel to a naive description we also give a mathematical model. Some—but not too many—of the following sections are accessible without a mathematical formalism. Therefore readers without mathematical background should not get frightened, but simply skip the mathematical sections. But bear in mind that cryptology is a mathemtical science, and don't expect to become a cryptology expert without struggling with the maths.

The purpose of this construct is that nobody can invert the encryption function except people who know the key. That is, an encrypted message (or a text, a file, ...) is kept secret from third parties. These can see that there is a message, but they cannot read the contents of the message because they don't have the key and therefore don't know which of the functions from the family to choose.

The sender and the receiver must know the key. Therefore they need a secure channel over which they can share it. In practice they negotiate the key in advance during a personal meeting. In Part III of this lecture notes we'll see other methods for negotiating keys.

Some cryptographically relevant alphabets:

• {A, B, ..., Z} = the standard alphabet of classic cryptography,
• {0, 1} = the alphabet of bits. The earliest appearence (after BAUER) is BACON 1605.
• The alphabet of bytes (= blocks of 8 bits, correctly: octets, because in early computers bytes did not necessarily consist of exactly 8 bits). The earliest appearance seems to be at IBM around 1964.
• More generally the alphabet of l-bit blocks
  [often l = 64, for example in DES or IDEA, or l = 128, in AES, see Part II].

Sometimes the alphabet is represented (or »encoded«) by the numbers 0, 1, 2, ...

For the standard alphabet: A ↔ 0, B ↔ 1, ..., Z ↔ 25.

Historically the assignment of numbers to the letters of the standard alphabet started with A ↔ 1. Such assignments go back to antiquity where they were abused for all kinds of mysticism. The first European use in the context of cryptography for an arithmetical description of a cipher apparently was by COMIERS (however in the Orient already by Ibn DUNAINIR in the early 13th century and Ibn AD-DURAIHIM):

• Claude COMIERS: L'Art d'Écrire et de Parler Occultement et sans Soupçon. Paris 1690.

Another work that uses the encoding of letters by numbers was recently unearthed by Joachim von zur GATHEN (Friedrich Johann Buck: Arithmetic puzzles in Cryptography. Cryptologia XXVIII (2004), 309 - 324) and put online:

• Friedrich Johann BUCK: Mathematischer Beweiß: daß die Algebra zur Entdeckung einiger verborgener Schriften bequem angewendet werden könne. Königsberg 1772.

[A saying of ten words is hidden in divine Holy Scriptures that every Christ is obligated to know and to follow. Who wants to know it should denote the alphabet by numbers. That is A by 1, ...]