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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
 

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Related Links (Outside this Site)

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

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  (2012-07-17)
Shamir's Secret Sharing (10:35)  by  Matt Parker  (standupmaths, 2019-12-31)

 
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Ciphers and Codebreaking


(2012-11-21)   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 ABCDEFGHIKLM NOPQRSTVXYZ
Ciphertext DEFGHIKLM NOPQRSTVXYZ ABC

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ROT13  is the only symmetrical shift cipher in the Latin alphabet of  26  letters.
ABCDEFGHIJKLM NOPQRSTUVWXYZ
NOPQRSTUVWXYZ ABCDEFGHIJKLM

Wikipedia :   Caesar cipher   |   ROT13


(2012-11-21)   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)


(2017-04-19)   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


(2017-04-14)   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


(2012-11-21)   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 (2017-04-14)   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)


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

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Wikipedia :   Rotor machines


(2012-11-21)   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


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

On 1945-09-01, 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)


(2017-04-09)   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, 2013-12-22).


(2012-12-22)   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


(2020-06-09)   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, 2018-01-11).

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