Final Answers
© 2000-2020 Gérard P. Michon, Ph.D.

Cryptography

I had a polynomial once. My doctor removed it.
Michael Grant (1954-) Gone, 2008.
Michon

Related articles on this site:

Related Links (Outside this Site)

History of Crypyography by Ashton Scheshan Gangadeen (2016年05月14日).
A primer on elliptic-curve cryptography by Nick Sullivan (2013年10月24日).

Wikipedia : Cipher | Cryptography | History of cryptography | One-time pad | Public-key cryptography
Elliptic curve cryptography (ECC) | RSA | Olive Hazlett (1890-1974, PhD 1915)

Lock Picking 101 (1:04:09) by Andrews Roy (2012年07月17日)
Shamir's Secret Sharing (10:35) by Matt Parker (standupmaths, 2019年12月31日)

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Ciphers and Codebreaking


(2012年11月21日) Simple Shift Ciphers: The easiest codes to break.
Caesar's cipher. Augustus cipher. Modern ROT13.

Strictly speaking, Caesar's cipher was a fixed monalphabetic substitution method based on the Roman alphabet (Classical Latin alphabet) of 23 letters (omitting J, U and W from the modern Latin alphabet of 26 letters). It consisted in replacing every letter by the letter appearing three ranks further in the alphabet:

Caesar's cipher used the Roman alphabet of 23 letters :
Plaintext A B C D E F G H I K L M N O P Q R S T V X Y Z
Ciphertext D E F G H I K L M N O P Q R S T V X Y Z A B C

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ROT13 is the only symmetrical shift cipher in the Latin alphabet of 26 letters.
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
N O P Q R S T U V W X Y Z A B C D E F G H I J K L M

Wikipedia : Caesar cipher | ROT13


(2012年11月21日) Monoalphabetic Substitution Cipher
Each letter of the alphabet is replaced by another (bijectively).

Frequency analysis is almost enough to break such a code.

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Wikipedia : Substitution cipher | Frequency analysis | Al-Kindi (c.801-873)


(2017年04月19日) Transposition Ciphers. Tricode.
Permuting the order of the plaintext letters.

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How to Write in Tri Code

Wikipedia : Classical cipher | Transposition cipher


(2017年04月14日) Disk Ciphers

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Alberti Cipher Disk (1467)

The device designed by Leon Battista Alberti (1404-1472) was used for secret transmission within the Vatican. It uses two different extensions of the Latin alphabet for the plain text and the cipher text.

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Alberti's Cipher Disk


(2012年11月21日) The Vigenère Cipher
A polyalphabetic cipher devised by Blaise de Vigenère.

It was once known as le chiffre indéchiffrable (the unbreakable cipher). It was re-invented many times and its good reputation is not deserved: The so-called Babbage-Kasisky method cab easily crack it, at least if the encoding key is much shorter than the text.

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Vigenère cipher | Giovan Battista Bellaso (b. 1505) | Blaise de Vigenère (1523-1595)
Babbage-Kasiski method | Friedrich Kasiski (1805-1881) | Charles Babbage (1791-1871)
Codebreaking challenge & solution by James Grime.


Arms of Thomas Jefferson (2017年04月14日) Bazeries Cylinder (Thomas Jefferson, 1795)
Secret-key cryptography for very short messages.
  • Thomas Jefferson's wheel cypher : 36 numbered disks of 26 letters.

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Wikipedia : Cylinder cipher | Etienne Bazerie (1846-1931) | M-94 (1922-1945)


(2017年04月14日) Rotor Machines
The most celebrated example is the German Enigma.

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Wikipedia : Rotor machines


(2012年11月21日) The German Enigma machines.
Codes broken by Poland and the UK before and during WWII.

The enigma machine was invented in 1918 by Arthur Cherbius (1878-1929). In spite of its high cost, it was eventually adopted by the German military once it was revealed that the British had been able to crack the military German codes during WWI (that revelation was published in a book by Winston Churchill).

Instrumental in that German decision to adopt a new coding technology was the future Panzer General Rudolf Schmidt (1886-1957) whose younger brother Hans-Thilo Schmidt (1888-1943) would eventually sell enigma secrets to a French operative codenamed Rex, under the cryptonym of Asché or Source-D.

The information received from Asché was communicated to the Polish cipher-bureau who could use it to figure out the internal wiring of the enigma rotors. The Polish mathematician Marian Rejewski (1905-1980) used this, together with the weakness introduced by the systematic repetition of the first trigram in the original standard Enigma protocol, to crack enigma codes in 1932.

Poland communicated that information back to France and the UK, where Alan Turing (1912-1954) could crack the codes even after the Germans had stopped repeating the first trigrams in their messages (in a way, Rejewski's ultimate contribution was to convince the British that enigma codes were breakable even if fewer weaknesses could be exploited).

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The Enigma Code by David Perry (NSA).
Turing: Pioneer of the Information Age by Jack Copeland
A genuine WWII Enigma machine presented by James Grime.

Wikipedia : Enigma machine | Enigma rotors | Lorenz SZ (Tunny) | Ultra


(2017年04月14日) One-time pad (OTP). Provably secure cryptosystem.
A truly-random secret key longer than the plaintext is used only once.

On 1945年09月01日, Claude Shannon published a classified paper demonstrated that a truly random one-time pad achieves perfect secrecy.

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One-time pad (1882) | Frank Miller (1842-1925) | Gilbert Vernam (1890-1960) | Joseph Mauborgne (1881-1971)


(2017年04月09日) Backdoors
A government may provide encryption methods which it can break.

Elliptic curve cryptography.

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NSA Surveillance (10:58) Controversy (4:19) by Edward Frenkel (Numberphile, 2013年12月22日).


(2012年12月22日) The mysterious Voynich manuscript :
Written on fine parchment carbon-dated between 1408 and 1438.

In 1912, this 200-page manuscript was acquired from Villa Mondragone, near Rome, by an antiques dealer from London who would move to New-York in 1914, Wilfrid Voynich (1865-1930). Né Michal Habdank-Wojnicz, he was a Polish-Lithuanian revolutionary who had escaped from penal servitude in Siberia and established himself in London in 1890. In 1898, he married Ethel Lilian Boole (1864-1960) daughter of Mary Everest Boole (1862-1916, niece of George Everest) and of the great mathematician George Boole (1815-1864) who died when she was 4 months old...

This mathematical connection may have played a rôle in building the early belief that the manuscript was written in some common language but encoded with a secret cipher to hide sensitive information not meant for the uninituated. This hypothesis is all but abandonned now.

What's now believed by an increasing number of scholars and amateurs alike is that the manuscript is a unique sample of a script invented to transcribe an unidentified Indo-European language or dialect for which no other script is known. The many botanical and astronomical illustrations in the Voynich manuscript offer some hope of identifying some scientific words and their Indo-European roots. This leads to a partial decoding of the Voynich alphabet in terms of associated sounds.

Along those promising lines, Stephen Bax has tentatively identified 10 words and 14 letters (or groups of letters). (video 47:11).

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National Geographic's "Naked Science" The book that can't be read by Walter Köhler and Martin Mészàros.
Arbëreshë people and Arbërisht, or extinct slavic language: | 1 | 2 | 3 | 4 | update | by Amy Michelle Mosier.
How to solve the Voynich manuscript, by Volder Z. : phonetics & alphabet | putting the pieces together


(2020年06月09日) Diffie-Hellmann key exchange (1976)

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Diffie-Hellman key exchange | Whit Diffie (1944-) | Martin Hellman (1945-)

The Mathematics of Diffie-Hellman Key Exchange (13:32) by Gabe Perez-Giz (PBS Infinite Series, 2018年01月11日).

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