History of cryptography

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Cryptography describes the encryption of messages or data for the purpose of secrecy. The history of cryptography can be divided into three epochs . In the first, encryption was carried out by hand (for example “with paper and pencil” or with mechanical disks ) , in the second (around 1920 to 1970) special machines were used, and in the third (around 1970) computers played a central role . The cryptanalysis (in more recent publications: cryptanalysis ) forms the complementary counterpart to cryptography. Methods are being researched to analyze cryptographic processes and break them if possible ( deciphering ). Cryptography and cryptanalysis are sub-areas of cryptology .

Only a few old systems are known from cryptography. New discoveries of documents from antiquity and antiquity as well as the opening of archives and interviews with contemporary witnesses allowed us to expand our knowledge of cryptographic systems of the past.

Age of encryption by hand

antiquity

The epoch of antiquity encompassed roughly the middle of the 4th millennium BC. BC to 6th century after the birth of Christ. The earliest use of cryptography can be found in the third millennium BC. In ancient Egyptian cryptography of the Old Kingdom . The main motif of the encryption of ancient Egyptian mythological and religious texts based on the principle of rebus and acrophony was the taboo on public pronunciation of various deities. The same was true for the writing area, which is why other hieroglyphs were used in these cases . In addition, the priests saw themselves in an elitist role and therefore watched over the secret knowledge of the gods, which resulted in the encryption of magical texts . These operations can be regarded as the first documented cases of encryption.

There are a few more ancient cases of encryption that are documented:

  • Around the year 1500 BC A potter in Mesopotamia made a clay tablet on which he wrote down the recipe for a glaze in different letters.
Skytale of the ancient Greeks
  • The Greeks are also already using cryptography. With the Skytale they developed in the 5th century BC. A cipher rod based on the principle of transposition .
  • Julius Caesar (around 100 BC to 44 BC) is said to have used the Caesar cipher named after him , which shifts each letter in the alphabet by a specified value.
  • The cipher is one of 64 arts described in the Indian Kamasutra (around 200 to 300 AD). The rule Mūladevīya assigns new letters to certain letters of an alphabet.

middle Ages

It was not until the end of the 20th century that it was recognized that between the years 500 and 1400 there were significant contributions to cryptography, especially from the Arab world, that had not been taken into account in modern research. The first book on this subject was written by the Islamic theologian and philosopher al-Kindī , who was also the first to describe statistical methods for cryptanalysis .

In Europe, however, there were few innovations in cryptography. Charlemagne (747 or 748–814) is said to have used an unknown alphabet as an encryption method in conjunction with a simple substitution (also called replacement method). The use of such a method is also said of St. Hildegard von Bingen (1098–1179). The "Isruna tract" is known due to 5 manuscripts from the 9th-11th centuries. Century. In this “ice rune treatise”, the characters in question are identified by determining their position in a given system. The only European scholar of whom a treatise on cryptography has come down by name from this period was the English monk and polymath Roger Bacon (1214–1292 or 1294). He listed seven encryption methods, including the omission of vowels and the use of an unknown alphabet.

Modern times

Like many other sciences, cryptography experienced a significant boom with the beginning of the Renaissance (around the end of the 14th century to the early 17th century). The procedures, which have hardly changed for thousands of years, have been further developed during this time.

Encryption disk

The most important development from this period is the cipher disk , which was described in 1466 by the Italian Leon Battista Alberti (1404–1472). In Italy at that time there were several warring city-states that encrypted important messages for fear of other readers. This made Italy the leading cryptography nation of the time. Giambattista della Porta (1535–1615) used unusual characters and thus an unknown alphabet on his cipher disk from 1563. The technique of unipartite simple substitution was used. The cipher sliders followed a similar principle . For example, in England at the time of Elizabeth I (1533–1603), two rulers that could be moved against each other were used for encryption. In the 19th century the gate valves were called Saint-Cyr gate valves . Cipher sticks served the same purpose.

Vigenère cipher

Blaise de Vigenère (1523–1596) published the tabula recta taken from the German Benedictine Abbot Johannes Trithemius (1462–1516) in 1508 in the fifth volume of his six-volume work Polygraphiae libri sex (German: Six books on polygraphy) written in Latin under his own name. This Vigenère cipher, published under a false name, was long considered unbreakable and was only systematically deciphered by Charles Babbage after almost 300 years . Finally, in 1863 , Friedrich Wilhelm Kasiski published a process named after him for determining the length of a key word and deciphering the process.

Babington plot

Both cryptography and cryptanalysis play a role in the Babington conspiracy during the reign of Queen Elizabeth I. The Babington conspiracy takes its name from Anthony Babington, who in 1586 planned together with a group of Catholics friends, the Protestant Queen Elizabeth I of England to assassinate and free Mary Stuart from prison and bring her to the English throne. Maria received letters from her followers, which were encoded with a nomenclator .

Unfortunately for the conspirators, the messenger Gilbert Gifford was a spy for Queen Elizabeth, who made sure that all letters were sent to Francis Walsingham, Elizabeth's security minister. Since the letters were encrypted, Walsingham hired the experienced code breaker Thomas Phelippes as secretary, who succeeded in deciphering the messages with the help of frequency analysis. Through the letters the news of the planned murder of Elisabeth came to light. Walsingham waited, however, because he wanted to know the names of everyone involved. To achieve this, he gave Phelippes the job of forging letters from and for Maria and adding another text to them. On July 17, 1586, Maria responded to the conspirators, thereby signing her own death warrant. The conspirators were caught just a month later and executed on September 20, 1586. To this day it is not clear whether the letters actually come from Maria Stuart.

Voynich manuscript

Page of the Voynich manuscript

Probably around the year 1500 the most discussed object in the history of cryptography was created to this day: the Voynich manuscript . It is a 224 page book written in an unknown script. Statistical studies indicate that this is not a book written in a natural language, but that it is encrypted (unless it is a meaningless sequence of letters). This encryption has not yet been resolved. Recent research suggests a meaningless sequence of letters.

19th century

Beale cipher

Also unsolved is the so-called Beale cipher , which supposedly reveals the location of a gold pot. A certain Thomas J. Beale is said to have hidden this treasure in the years 1820/22, whereupon he gave the encrypted description of the location to a confidant, through whom it became publicly known after a few decades. One of three parts of the Beale cipher could be deciphered using the American Declaration of Independence . The numbers represent the first letters of the nth words in the original text. The other two parts have not been resolved to this day, and the treasure has not yet been found.

The Beale cipher has already employed some cryptanalysts and treasure hunters. Due to various inconsistencies, however, it is now assumed that the treasure does not actually exist and that the entire story is made up.

Dorabella cipher

At the end of the 19th century, another cryptographic puzzle emerged that has not yet been solved: the Dorabella cipher . This is a code that the English composer Edward Elgar used in a letter in 1897. Edward Elgar, fascinated by puzzles and ciphers, had already had a long correspondence with Dora Penny (* 1877), who was twenty years his junior, when on July 14, 1897 he enclosed a note with cryptic characters on one of his letters. Elgar used 20 different characters on three lines.

Cryptography in the Civil War

During the American Civil War (1861–1865), telegraphy was already used, but the importance of data encryption and decryption were still underestimated. There was no coordination in the field of cryptography on either side of the conflict, let alone qualified experts. Which procedure was used for which purpose was therefore at the discretion of the respective commander. Although both sides invested little effort in cracking the codes of the other side, numerous decipherments were achieved.

Further development through the advent of telegraphy

At the end of the 19th century, the widespread use of the telegraph (which one could easily tap and eavesdrop on) led to new considerations in cryptography. Auguste Kerckhoffs von Nieuwenhof formulated a principle of cryptography with the Kerckhoffs' principle named after him, according to which the security of a cryptographic procedure should be based solely on the secrecy of the key - the procedure itself does not have to be kept secret and, on the contrary, can be published and published by many experts are examined. Kerckhoffs' principle is an important principle of cryptography to this day, which is also adhered to when encrypting on the Internet.

First World War

Zimmermann dispatch

During the First World War, comparatively simple procedures that could be carried out by hand with paper and pencil were still used for tactical purposes . The best known was called ADFGX . The French artillery officer Capitaine Georges Painvin managed to crack ADFGX in April 1918 (shortly before and during the German spring offensive). According to a number of historians and cryptologists, he made a significant contribution to the fact that German soldiers did not succeed in taking Paris in the First World War.

The First World War is considered to be the first war in which the possibilities of cryptanalysis were systematically used. The effort that the warring parties made to decipher opposing radio messages increased significantly in the course of the war, after some states had not operated any deciphering units at all at the beginning of the war. The development of new encryption methods could not keep up with this development, which is why almost all of the methods used in World War I were cracked with comparatively little effort.

At a higher level, code books were mainly used during World War I , with which every word of a text was converted into an incomprehensible other word or number. On January 19, 1917, Arthur Zimmermann , the Foreign Minister of the German Reich, sent a telegram encoded in this way to the German ambassador in Mexico. In this telegram, known as the Zimmermann Telegram, the government of Mexico was offered territorial gains in the United States if it entered the war on the German side. The telegram was intercepted and deciphered by the British secret service (see also: SMS Magdeburg signal book ). The Telegram forced the United States to rethink its policy of neutrality and, ultimately, was instrumental in mobilizing the public to join the war.

The era of machine encryption

Forerunner: The Machina deciphratoria by Gottfried Wilhelm Leibniz

Another “calculating machine” from Gottfried Wilhelm Leibniz remained concept: the Machina deciphratoria . He invented the cipher machine back in the late 1670s, but it was not until 1688 that it was described in a brief for an audience with Emperor Leopold I in Vienna. "In doing so, he anticipated the principle of the rotor key machine by Arvid Damm (1869–1927), according to which the first generation of mechanical encryption machines (from 1918) worked, by almost 200 years."

In the years 2010–2011, Nicholas Rescher reconstructed the principle from Leibniz's notes and Klaus Badur implemented the design in detail, on the basis of which the functioning device was built in 2014 by the company G. Rottstedt in Garbsen. Emperor Leopold did not consider Leibniz's offer any further, as his advisors considered their procedures (wrongly) safe.

How it works: “For the Leibniz machine, the key consists of a) an assortment of six cipher alphabets that are to be placed on the drum together with the associated deciphering alphabets; b) the indication of which of twelve possible gap gears is used; c) the starting position of this gap gear. For the six cipher alphabets you can basically choose from 26! = 1 × 2 ×… × 26 ≈ 4 × 10 26 possibilities. Realistically, the diplomat would hardly have been given more than 50 alphabet pairs in the secret case. But as long as the spy cannot get hold of the suitcase, he has to consider the full range of possibilities. And even with 50 alphabet pairs, 50! / (50 - 6)! = 11,441,304,000 options for mounting them on the drum - including the order of the strips. "

The 20th century

The devastating experiences of World War I meant that the first encryption machines were developed during the war and in the years after . These offered a significantly higher level of security than the manual methods customary up to that point. The numerous encryption machines, which now heralded a new era in cryptography history, should not hide the fact that (mainly for cost reasons) numerous manual procedures were still used for the time being - even if mostly only for less important purposes.

One-time pad

The invention of the one-time pad also occurred at the time of the first machine developments. With this method, the text is encrypted character by character together with a random string that is only used once. If it really is a random sequence, every encryption result is equally likely. In this sense, the procedure is mathematically safe. The engineer Gilbert Vernam (1890–1960), who first presented the idea in 1918, is considered to be the inventor. The American Joseph O. Mauborgne (1881–1971) implemented this idea and coined the term “One-Time Pad” (German: one-time block). Shortly afterwards, the Germans Werner Kunze, Rudolf Schauffler and Erich Langlotz also worked on this method. Born around 1890, Kunze was a mathematician like Schauffler and, after successfully working as a cryptographer in the First World War, joined the cipher service of the Foreign Office in 1918 . In 1921, the German cryptographers suggested using blocks that were printed with randomly generated digits to encode the diplomatic codes of the time and referred to them as i-worms (individual worms). This method was actually used by the diplomatic service of the Weimar Republic.

The one-time pad quickly became popular, especially since the process could be used both by machine and by hand. During World War II, the Red Chapel in France used a process of using a hard-to-get book instead of a random sequence. When the German Abwehr was able to get this book anyway, they were able to decipher all overheard radio messages retrospectively. With today's resources, this type of encryption could be cracked statistically - the bigram 'en', for example, is more common than the bigram 'xa'.

The one-time pad was likely used on the red phone during the Cold War. What is certain is that many spies used this method. They received small pieces of paper with rows of random numbers from their chief agents, which served as keys. The spy could do the encryption or decryption manually. This procedure was safe and unsuspicious, as no conspicuous aids were required in addition to the note.

Kryha machine

The Kryha encryption machine impressed with its visually appealing design, but it was unsafe

Born in Ukraine, Alexander von Kryha came to Germany in the mid-twenties and developed an encryption machine (Kryha machine) there, which he tried to sell using marketing methods that were modern for the time. The machine was easy to use and, unlike other encryption devices of the time, looked elegant and of high quality. The security of the machine was checked by the mathematician Georg Hamel , who calculated the size of the key space. The supposedly high level of security, however, turned out to be deceptive. In 1933, William F. Friedman, together with Solomon Kullback , Frank Rowlett and Abraham Sinkov, was able to decipher a Kryha-encrypted message consisting of 1135 characters within two hours and 41 minutes. Despite the weakness of the machine, which was proven by this, it was still in use until the 1950s.

Hagelin machines

an M-209

The Swede Boris Hagelin (1892–1983) developed into a successful entrepreneur in the field of encryption machines. Hagelin finished his studies in Stockholm in 1914 and then worked in Sweden and the USA. His father was a co-owner of the company AB Cryptograph, which built rotor cipher machines based on the patent from Arvid Damm. In 1927 Hagelin took over the company, reorganized it and changed the name to AB Cryptoteknik. The Hagelin machines are known for their unique drum-and-lug mechanics. His most successful encryption machines were the M-209 in World War II and the C-52 in the Cold War, which was very popular and sold in more than 60 countries.

German cryptography in World War II

During World War II, the Germans used at least seven different encryption machines:

  • Enigma : see below
  • Lorenz key machine : This telex key machine, used at the highest military level, was cracked by the British with the help of the computer forerunner Colossus .
  • T52 : This telex key machine , which is also used for important messages, was cracked in an early version by the Swedish mathematician Arne Beurling.
  • T43 : The T43 implemented a one-time pad and was therefore theoretically unbreakable.
  • Cipher device 39 : This machine was a further development of the Enigma, but its development was discontinued in favor of the cipher device 41.
  • Key device 41 (Hitlermühle): The Hitlermühle was a German further development of a Hagelin machine that was supposed to replace the Enigma. However, it was no longer used on a large scale.
  • Hellschreiber , a secret writer from Rudolf Hell : Little is known about this machine.

Manual systems continued to be used in areas where machine use was not possible or too expensive.

Enigma

The German encryption machine Enigma

The ENIGMA was applied for a patent by Arthur Scherbius on February 23, 1918 and was initially marketed commercially. At the end of the 1920s, the German military became increasingly interested in the machine. The general military armament from 1933 onwards contributed to the intensive use of the ENIGMA. In the end, tens of thousands were deployed in the Second World War and were mistakenly considered “unbreakable” on the German side .

After Polish listening stations intercepted a German radio message encrypted with ENIGMA for the first time on July 15, 1928, and after the Polish cryptanalyst Marian Rejewski was able to uncover the internal wiring of the rotors in 1932 , the Biuro Szyfrów (Polish encryption service) succeeded at the turn of 1932/33 the first ENIGMA decipherments . In 1939 they inaugurated their British and French allies at the Pyry meeting and gave them Polish replicas of the ENIGMA . The British code breakers around Alan Turing were extremely successful during the Second World War in deciphering the German radio messages intercepted with the help of the Y-Stations . To do this, they used a special electromechanical "cracking machine" called the Turing bomb . From January 1940 the German ENIGMA radio traffic was continuously "read" with only a few exceptions.

US cryptography in World War II

The Americans used the M-209 developed by Boris Hagelin during World War II. It was a comparatively small and handy machine that was built in large numbers. The Germans managed to crack this machine with the help of a special deciphering device.

SIGABA was used for more important messages . This was a Rotor encryption machine that functioned similarly to the Enigma but was more secure. As far as we know today, the SIGABA was never cracked.

The Navajo Code also played an important role . The Navajo code was an encryption method used during the US Pacific War against Japan from 1942 onwards, which was based on using members of the North American Indian tribe of the Diné (also Navajo) as code speakers. They translated the military instructions into their native Navajo language , which belongs to the Na-Dené language family . This is not related to any European or Asian language and made the Navajo Code so impenetrable.

American deciphers achieved great success in World War II. The deciphering of the Japanese PURPLE should be mentioned here in particular . After the first intrusions into Japanese code systems around 1940, PURPLE was gradually unraveled by a group led by the American mathematician and cryptologist William Friedman . Later it was possible to recreate the machine and to decrypt radio messages as part of the MAGIC campaign. In December 1941 a radio message encrypted with PURPLE was overheard and decrypted. The 14-part text contained the breakdown of diplomatic relations and was ultimately the declaration of war before the attack on Pearl Harbor . Delays in the evaluation and forwarding of the information prevented a timely warning; the message reached the naval base by means of a regular civilian telegram after the attack.

After the Second World War

Soviet Fialka machine

In the period after the Second World War, the sources of military proceedings deteriorated as most of the relevant information was classified as secret. Countries that did not develop their own cryptographic technology mostly relied on the encryption machines manufactured by Hagelin, which achieved a high level of security in the 1950s. From around 1970, electronic devices took over this task, which marked the beginning of the computer era in cryptography.

The age of modern cryptography began with Claude Shannon , possibly the father of mathematical cryptography. In 1949 he published the article Communication Theory of Secrecy Systems. This article, along with his other work on information and communication theory, established a strong mathematical basis for cryptography. The open scientific discussion about the encryption method thus became the core of the development, while tactics such as security through obscurity were relegated to their places.

VENONA project

The VENONA project was a joint project between the US secret services and MI5, the UK secret service, to decipher Soviet secret messages. The successes achieved through the project are the last significant military cryptanalysis successes that are publicly known. In the period from 1942 to 1945, the US Army Signal Security Agency (SSA) heard and stored a large amount of Soviet messages. Although the messages were encrypted with the (actually unbreakable) one-time pad, around 2,200 messages were decrypted and translated over the course of 40 years. The Soviet side had used the one-time-pad method incorrectly. As the name suggests, each individual secret key can only be used once. However, the Soviets used them multiple times to encrypt various messages. In the early years of the Cold War, this was a major source of US espionage activity.

Age of encryption with computers

In the 1970s, cryptography changed from a pure secret science to a research discipline that was also carried out publicly. This is mainly due to the fact that with the advent of computers, there has been an increasing demand for data encryption.

Data Encryption Standard (DES)

In 1976 there were two major advances. First, there was the DES ( Data Encryption Standard ) algorithm developed by IBM and the National Security Agency (NSA) to create a secure, unified standard for inter-agency encryption (DES was founded in 1977 under the name FIPS 46-2 (Federal Information Processing Standard) published). DES and more secure variants of it (3DES) are still used today. B. used for banking services.

Public key cryptography

The second and more important advance was the publication of the article New Directions in Cryptography by Whitfield Diffie and Martin Hellman in 1976 ( Diffie-Hellman key exchange ). This paper introduced a radically new method of key distribution and initiated the development of public key procedures. The key exchange is one of the fundamental problems of cryptography. One of the best-known public key methods was the RSA cryptosystem , or RSA for short (by Ronald L. Rivest , Adi Shamir , Leonard Adleman ) in 1977 . It is an example of an asymmetric cryptosystem .

Before this discovery, keys were symmetrical, and possession of a key allowed a message to be both encrypted and decrypted. Therefore, the key had to be exchanged between the communication partners in a secure way, for example by a trustworthy courier or when the communication partner met directly. This situation quickly became unmanageable as the number of people involved increased. A new key was also required for each communication partner if the other participants were not able to decrypt the messages. Such a procedure is referred to as symmetrical or also as a “secret key”, “shared secret” or “private key” procedure.

Public key cryptography uses a pair of matching keys. One is a public key which - in the case of an encryption process - is used to encrypt messages for the key holder. The other is a private key that must be kept secret by the key holder and is used for decryption. Such a system is called asymmetric, because different keys are used for encryption and decryption. With this method, only a single key pair is required for each participant, since possession of the public key does not compromise the security of the private key. Such a system can also be used to create a digital signature. The digital signature is calculated from the data to be signed or its hash value and the private key. The correctness of the signature - and thus the integrity and authenticity of the data - can be checked by appropriate operations with the public key. Public key methods can also be used for authentication in interactive communication.

Public-key cryptography was developed in secrecy by the military before public research achieved it. On December 17, 1997 the British GCHQ (Government Communications Headquarters in Cheltenham) published a document in which they stated that they had found a public key method before the Diffie and Hellman article was published. Various classified documents were written in the 1960s and 1970s by James H. Ellis , Clifford Cocks and Malcolm Williamson , among others , which led to designs similar to those of RSA and Diffie-Hellman.

The security of factorization-based public key cryptography lies in the use of a product of large prime numbers which serves as the public key. The private key consists of the associated prime factors or values ​​derived from them. The decomposition of a sufficiently large public key is considered impractical due to the mathematically very complex factorization.

In particular after the introduction of elliptic curve cryptography in the 1980s, advanced number theoretic methods were used in cryptography.

Pretty good privacy

PGP inventor Phil Zimmermann

In the age of the Internet, there was also a loud call for private encryption. So far, it has been governments and global corporations who have been able to use RSA encryption due to the need for powerful computers. The American physicist Phil Zimmermann then developed RSA encryption for the general public, which he called Pretty Good Privacy (PGP) and published it on Usenet in June 1991. A new feature of this procedure was the ability to sign an email with a digital signature that clearly identifies the originator of the message.

Advanced Encryption Standard (AES)

In January 1997, the search for a successor to the DES standard began. What was new was that a company was no longer to develop the algorithm together with the NSA, as was the case with DES, but that cryptologists from all over the world could make suggestions that were then publicly analyzed. After two conferences in 1998 and 1999, five of the original fifteen proposals remained ( MARS , RC6 , Rijndael, Serpent , Twofish ), of which at the last conference in 2000, Rijndael was selected as the new AES because of its superior speed.

additional

The efforts of the US government in the 1990s to prevent the private encryption of data made a name for themselves as Crypto Wars .

reception

Cryptography in Fiction

There are numerous books and films in which cryptography plays an important role. The following films are mentioned:

A selection of novels follows:

Cryptography history as a research subject

The US historian David Kahn is considered the founder of cryptography historical research . His book "The Codebreakers" (first edition 1967) looked at the topic systematically for the first time and is still considered a standard work today. Today, the history of cryptography is a very active area of ​​research, with new discoveries being made every year. The quarterly US magazine Cryptologia is the most important publication for new research results . The interests of the research scene are mainly focused on the period from 1920 to the present day. Many of the findings of cryptography historical research come from amateur researchers. Despite significant progress in recent years, there are still large gaps:

  • The background of the Kryha machine (especially the biography of Alexander von Kryha) has hardly been researched.
  • So far, comparatively little is known about the history of cryptography in the GDR.
  • Little is known about the cryptography of the Soviet Union either.

Simulators

Simulation programs are now available for numerous historical encryption methods. Mention should be made at this point of the open source software CrypTool , which in addition to modern processes also supports several manual processes and Enigma encryption.

literature

Web links

supporting documents

  1. ↑ Cf. Alexandra von Lieven : Plan of the course of the stars - the so-called groove book . The Carsten Niebuhr Institute of Ancient Eastern Studies (among others), Copenhagen 2007, ISBN 978-87-635-0406-5 .
  2. ↑ a b c d e f g h Friedrich L. Bauer: Deciphered secrets. 3rd, revised and expanded edition. Springer, 2000, ISBN 3-540-67931-6
  3. ↑ a b c d e David Kahn: The Codebreakers: The Comprehensive History of Secret Communication from Ancient Times to the Internet. Scribner, New York, Rev Sub edition, 1996.
  4. ↑ Al-Kadi, Ibrahim A .: The origins of cryptology: The Arab contributions. In: Cryptologia, 16 (2) (April 1992), pp. 97-126.
  5. ^ Klaus Düwel : Runenkunde. 3. Edition. Metzler, Stuttgart Weimar 2001, ISBN 3-476-13072-X .
  6. ↑ a b Simon Singh: Secret Messages. The art of encryption from ancient times to the Internet. Hanser 1999.
  7. ↑ Klaus Schmeh: 'The hunters of the encrypted treasure'. Telepolis 2007, https://www.heise.de/tp/artikel/26/26817/1.html
  8. ↑ Klaus Badur: The ancestors of the Enigma and the computer , in: Spectrum of Science September 2016, pp. 76–87; it includes: Nicholas Rescher: Leibniz's The Secret Machine , pp. 84–87; here: Rescher, p. 84
  9. ↑ Badur, p. 87
  10. ↑ Klaus Schmeh: Code breakers versus code makers The fascinating history of encryption. Publisher: W3l; 2nd edition, 2007.
  11. ↑ C. Shannon: Communication Theory of Secrecy Systems (PDF; 563 kB), 1949