Cipher Machines From Antiquity to the Enigma Machine

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Cipher Machines

From Antiquity to the Enigma Machine

Wayne Summers

Department of Computer Science

Columbus State University

Columbus, Georgia, USA


Abstract
More and more people worldwide are using the Internet for personal transactions. Many are transmitting personal data including credit card and identification numbers. This requires that a secure connection be established. This secure connection provides a mechanism for transmitting personal data in encrypted form so that others can not “read” the information. Encryption or encoding the data is not a new concept. “History is punctuated with codes. They have decided the outcomes of battles and led to the deaths of kings and queens.” [Singh, pg. x] This paper traces the history of machines for encryption from the earliest known encryption or cipher machines to the Enigma machine used in the first half of the 20th century.
Introduction to Cryptography and Encryption
The word cryptography comes from the Greek words kryptos meaning hidden and grafi meaning writing and is the study of hiding written information through encoding or enciphering. Singh [Singh, xii] explains that a code is the replacing of a word or phrase with a word, number or symbol, while a cipher involves making letter-for-letter substitutions. Information can be hidden by either substituting other letters, words or symbols for the letters or words in the message or transposing the letters or words in the message. Many of the modern cryptographic algorithms use combinations of substitutions and transpositions. Cryptology is the overall study of codes and ciphers and cryptoanalysis is the science of the decryption of codes and ciphers.

Encryption, or hiding the meaning of a message, appears to have begun in Egypt around 1900 BCE. The scribe for the Pharaoh Amenemhet II “used hieroglyphic substitutions to impart dignity and authority” to the inscriptions in the pyramids. [Higgs, pg. 3]

From around 1500 BCE to 500 BCE, Assyrian and other cultures including Mesopotamian, Indian, Chinese, and Egyptian began hiding information using a variety of methods including tattooing the message on the heads of the messengers, “carving” the message in the stomach of animals, and hiding the message under new wax. This was the beginning of steganography or hiding messages.
Around 600 BCE, the Hebrew scribes used a simple substitution cipher known as ATBASH. ATBASH uses a reverse alphabet where for example the third letter would be replaced with the third character from the end of the alphabet. This was used in writing the book of Jeremiah.
The first appearance of a cipher device is the scytale (Fig. 1) which was used by the Greeks around 475 BCE. The scytale consists of a staff of wood around which a strip of papyrus, leather, or parchment is tightly wound. The message is written down the length of the staff in rows. The parchment is unwound leaving what appears to be nothing more than a series of disconnected letters. The secret key to deciphering the text is the circumference of the wood. If you use a scytale with the wrong circumference, the message is unusable. If someone else intercepts the message and has a piece of wood with the right circumference they are able to read the message.

Figure 1 – Scytale [Stallings]


So the message

the scytale is a transposition cipher

becomes


THESN EPCSS OICAS PCASP YTIHT RTEAA IRLNO

Julius Caesar is reported to having developed a substitution cipher called the Caesar cipher. Each letter in the message is replaced with the letter that is three places further down the alphabet, looping back to the beginning of the alphabet when the end is reached. (Table 1).



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Table 1 – Caesar cipher table
The message

the caesar cipher is a substitution cipher

becomes

WKHFD HVDUF LSKHU LVDVX EVWLW XWLRQ FLSKH U


Cryptanalysis was developed by the Arabs around the 8th century A.D. by Abu 'Abd al-Rahman al-Khalil ibn Ahmad ibn 'Amr ibn Tammam al Farahidi al-Zadi al Yahmadi who solved a cryptogram in Greek for the Byzantine emperor and was the first to discover and write down the methods of cryptanalysis. Another Arab of the 9th century, Abu Yusuf Ya'qub ibn Is-haq ibn as-Sabbah ibn 'omran ibn Ismail al-Kindi wrote "A Manuscript on Deciphering Cryptographic Messages". In 1412, the Arabic knowledge of cryptology was fully described in the Subh al-a 'sha, a huge 14-volume encyclopedia, written by Shihab al-Din abu 'l-Abbas Ahmad ben Ali ben Ahmad Abd Allah al-Qalqashandi [Higgs, pp.9-11].

During the Middle Ages in Europe, encryption was primarily restricted to the monks. " Around 1250 A.D., Roger Bacon, wrote the "Epistle on the Secret Works of Art and the Nullity of Magic” which described seven deliberately vague methods of concealing a secret. Around 1392, Geoffrey Chaucer wrote six short passages in cipher in his "The Equatorie of the Planetis" notes to his "Treatise on the Astrolabe” [Higgs, 12-13].


Early Cipher Machines

By the 15th century, both cryptography and cryptoanalysis were in widespread use throughout Europe, especially in diplomatic communications. Except for the scytale, all of the encryption techniques required manual computations typically aided by writing down the tables. In addition, all of the substitution algorithms were monoalphabetic where each letter was mapped to only one other letter. This was changed by Leon Battista Alberti (1404-1472) when he developed a cipher machine for mechanical encryption [Fig. 2]. The machine is based on the Caesar cipher algorithm. During the 1460's, while walking through the gardens of the Vatican, Leon Alberti had a casual conversation about cryptography with the pontifical secretary, Leonardo Dato. Alberti developed and published the first polyalphabetic cipher and designed a cipher disk to simplify the process.  Cryptography historian David Kahn titles him the "Father of Western Cryptography", pointing to three significant advances in the field which can be attributed to Alberti: "the earliest Western exposition of cryptanalysis, the invention of polyalphabetic substitution, and the invention of enciphered code" [Wikpedia].



Fig. 2 – Alberti cipher disk [Higgs, 17]


Alberti described his invention:

"I make two circles out of copper plates. One, the larger, is called stationary, the smaller is called movable. The diameter of the stationary plate is one-ninth greater than that of the movable plate. I divide the circumference of each circle into 24 equal parts [called] cells. In the various cells of the larger circle I write the capital letters, one at a time in red, in the usual order of the letters [whilst those around the movable circle are] not in regular order like the stationary characters, but scattered at random. [I then] place the smaller circle upon the larger so that a needle driven through the centres of both may serve as the axis of both and the movable plate may be revolved around it." (Alberti, "Trattati in Cifra", 1470, cited in Kahn, 1996, pp127-128.)

Alberti then explained how he introduced "polyalphabetic substitution cipher" using his cipher disk:
"After writing three or four words, I shall change the position of the index in our formula by turning the circle, so that the index k may be, say, under D [] and all the other stationary letters [] will receive new meanings." (Alberti, "Trattati in Cifra", 1470, cited in Kahn, 1996, pp128-129.)
In 1586, Blaise de Vigenère (1523-1596) wrote a book on ciphers that described the Vigenère polyalphabetic algorithm. This method uses different monoalphabetic encryptions selected from a Vigenère square (Table 2) using a keyword. The keyword and Vigenère are shared between the sender and receiver of the encrypted message. Without the keyword you cannot define which cipher character belongs to the according plaintext character. You can use any agreed upon keyword you want.

For demonstrating the encryption method we choose the keyword "cipher" and use it with the plaintext we want to encrypt.

Keyword: CIPHERCIPHE  Plaintext: encrypt this!

Ciphertext: GVRYC GVBWP W


For getting this result you need to find the ciphertext letter in the matrix according to the x-axis (e) and the y-axis (C). The result is obviously G.

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Table 2 - Vigenère square
In the late-1790s, Thomas Jefferson built a polyalphabetic substitution wheel cipher machine [Fig. 3]. The wheel consists of 26 wooden disks threaded onto a spindle. Each disk can be turned separately and contains a scrambled alphabet inscribed on it. To encrypt a message, you would line up all of the letters of the plaintext message. Then select one of the other rows of letters and copy that as the encrypted message. The recipient of the encrypted message would need a similar device. The recipient would line up all of the letters of the encrypted message and then look for a row that has meaningful words in it. The major disadvantage to the wheel cipher machine is that a copy of the machine has to be distributed to everyone who will be receiving messages. Ironically, a French cryptologist devised a similar device in 1890, and the U.S. Army introduced an electrical version prior to World War I that was used until the early 1940s.

Figure 3 – Jefferson Cylinder



The Wheatstone Cryptograph (Fig. 4), originally invented by Wadsworth in 1817, but developed by Wheatstone in 1860's, comprised two concentric wheels with two hands. When the larger hand pointed to the plaintext letter, the smaller hand would point to its cipher equivalent. Because of the way the gears were arranged, the smaller hand would change after each letter was encrypted. This was used to generate a polyalphabetic cipher.




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