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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  (2016-05-14).
Aprimer on elliptic-curve cryptography  by Nick Sullivan  (2013-10-24).

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) 
Caesar's cipher.  Augustus cipher.  Modern ROT13.

Strictly speaking,  Caesar's cipher was a fixed monalphabetic substitution method based on the Romanalphabet  (Classical Latin alphabet)  of23 letters  (omitting J, U and W from the modern Latin alphabet of 26 letters).  It consisted in replacingevery letter by the letter appearing three ranks further in the alphabet:

Caesar's cipher used the Roman alphabet of  23  letters :
PlaintextABCDEFGHIKLMNOPQRSTVXYZ
CiphertextDEFGHIKLMNOPQRSTVXYZABC

 Come back later, we're still working on this one...

ROT13 is the only symmetrical shift cipher in the Latin alphabet of  26  letters.
ABCDEFGHIJKLMNOPQRSTUVWXYZ
NOPQRSTUVWXYZABCDEFGHIJKLM


(2012-11-21)  
Each letter of the alphabet is replaced by another  (bijectively).

Frequency analysis  is almost enough to break such a code.

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(2017-04-19)  
Permuting the order of the plaintext letters.

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(2017-04-14)  

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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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(2012-11-21)  
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 theencoding key is much shorter than the text.

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 Arms of Thomas Jefferson (2017-04-14)  
Secret-key cryptography for very short messages.

  • Thomas Jefferson's wheel cypher :  36 numbered disks of 26 letters.

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

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(2012-11-21)  
Codes broken by Poland and the UK before and during WWII.

The enigma machine was invented in 1918 byArthur 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 brotherHans-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 tothe Polish cipher-bureau who could use it to figure out the internal wiring of theenigma rotors. The Polish mathematicianMarianRejewski (1905-1980)used this,  together with the weakness introduced by the systematic repetition of the firsttrigram in the original standard Enigma  protocol,  to crack enigma codes in 1932.

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

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(2017-04-14)  
A truly-random secret key longer than the plaintext is used only once.

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

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(2017-04-09)  
A government may provide encryption methods which it can break.

Elliptic curve cryptography.

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(2012-12-22)  
Written on fine  parchmentcarbon-dated between 1408 and 1438.

In 1912, this 200-page manuscript was acquired fromVilla Mondragone, near Rome, by an antiques dealer from Londonwho 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 servitudein 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 ofGeorge Everest) and of the great mathematicianGeorge Boole (1815-1864)who died when she was 4 months old...

This mathematical connection may have played a rôle in building the early beliefthat the manuscript was written in some common language but encoded with a secret cipherto 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 thatthe manuscript is a unique sample of a script invented to transcribe an unidentifiedIndo-European language or dialect for which no other script is known. The many botanical and astronomical illustrations in the Voynich manuscript offersome 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 Baxhas tentatively identified 10 words and 14 letters  (or groups of letters). (video 47:11).

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(2020-06-09)  

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