AN INTRODUCTION TO CRYPTOLOGY

•

DEFINITIONS•Cryptology: The study of codes and ciphers, or the art of writing and solving them.•Cryptosystem: refers to a suite of algorithms needed to implement a particular form of encryption and decryption. Typically, a cryptosystem consists of three algorithms: one for key generation, one for encryption, and one for decryption.

DEFINITIONSTwo main branches of Cryptology-cryptography and cryptanalysis.•Cryptography: The science of secret writing with the goal of hiding the meaning of the message.•Cryptanalysis: The science of breaking cryptosystems. Cryptanalysis is the only way to ensure that a cryptosystem is secure.

‘CODES’ VS ‘CIPHERS’Ciphers are systems for disguising the meaning of a message by replacing each of the individual letters in the message with other symbols. Codes place more emphasis on meanings than characters, and tend to replace whole words or phrases according to a list contained in a code book.

PLAYING CARD CIPHERUse 2 suits from a standard playing deck (let’s say Diamonds and Clubs). There are 26 cards in those 2 suits, which match up nicely with the 26 letters of the alphabet.Diamonds: Ace (A), 2 (B), 3 (C), 4 (D), 5 (E), 6 (F), 7 (G), 8 (H), 9 (I), 10 (J), Jack (K), Queen (L), King (M)Clubs: Ace (N), 2 (O), 3 (P), 4 (Q), 5 (R), 6 (S), 7 (T), 8 (U), 9 (V), 10 (W), Jack (X), Queen (Y), King (Z)If you need more than 1 of certain letter, use another suit (for instance, if you need 2 K’s, use the Jack of Diamonds and the Jack of Hearts, since they are both red cards).If you need more than 2 of a certain letter, you would need another deck of cards (or another cipher!)

BOOK CIPHERA book cipher is a cipher in which the key is some aspect of a book or other piece of text. It is typically essential that both correspondents not only have the same book, but the same edition. Traditionally book ciphers work by replacing words in the plaintext of a message with the location of words from the book being used. In this mode, book ciphers are more properly called codes.

BOOK CIPHER

For example, if a book ciphertext contained “3512209”, that would refer to page 351, line 22, word 9. A book cipher can have problems; if a word appears in the plaintext but not in the book, it cannot be encoded. An alternative approach which gets around this problem is to replace individual letters rather than words. A famous use of a book cipher is in the Beale ciphers, of which document number 2 uses a (variant printing of) the United States Declaration of Independence as the key text.

THE ALBERTI CIPHERLeon Battista Alberti (1404 – 1472) was an Italian author, artist, architect, poet, priest, linguist, philosopher, and cryptographer. Alberti invented the first poly-alphabetic cipher which is now known as the Alberti cipher and machine-assisted encryption using his Cipher Disk.

THE ALBERTI CIPHERThe poly-alphabetic cipher was the most significant advance in cryptography since before Julius Caesar's time. The Alberti Cipher Disk embodies the first example of poly-alphabetic substitution with mixed alphabets and variable period.

THE ALBERTI CIPHERThis device is made up of two concentric disks, attached by a common pin, which can rotate one with respect to the other. The larger one is called Stabilis [stationary or fixed], the smaller one is called Mobilis [movable]. The circumference of each disk is divided into 24 equal cells. The outer ring contains one uppercase alphabet for plaintext and the inner ring has a lowercase mixed alphabet for ciphertext.

THE ALBERTI CIPHERThe outer ring also includes the numbers 1 to 4 for the super-encipherment of a codebook containing 336 phrases with assigned numerical values. This is a very effective method of concealing the code-numbers, since their equivalents cannot be distinguished from the other garbled letters. The sliding of the alphabets is controlled by key letters included in the body of the cryptogram.

THE ALBERTI CIPHERTo send an encrypted letter, the letters or numbers in a plaintext message were read on the outer plate and replaced with the corresponding letter on the inner plate. The sender and receiver both needed to have identical disks and decide on an initial position for the two disks relative to each other. This might seem like an ordinary substitution cipher, but the beauty and complexity was in what came next-after three or four words, the position of the index would change by turning the smaller disk (Mobilis).

TRIMETHIUS’ TABLEAUJohannes Trimethius was a German born abbott who produced the world’s first printed book on Cryptography. In the work he outlined a method for writing poly-alphabetic cipher systems, known as the Tableau.

TRIMETHIUS’ TABLEAUThe basis of Trimethius’ Tableau is this: write out a table that had 26 columns across and 26 rows down. Each row contains the alphabet in standard order, but in each successive row the alphabet undergoes a shift by one further place.

TRIMETHIUS’ TABLEAUTo write an enciphered message, he suggested using the first row for the first letter, then the second row for the second letter, and so on. Example: “ALL IS WELL” would become “AMN LW BKST”. Notice that the ‘L’s become different letters in the ciphertext. This makes the code more difficult to break than the Caesar Cipher or the Alberti Cipher.

CRYPTOLOGY 101

•

Do you want to learn more about Cryptology?

Then sign up for ‘Cryptology 101’ during the 8th period Enhancement.

See Mr. Hayden for more information.