Write as product of transpositions

Even more algorithms can be found here.

Write as product of transpositions

You start with the first pair of letters, "PL", and find them in the matrix. In this way "Playfair" is enciphered to "Jdcwunpe".

write as product of transpositions

If the letter pair is on the same row, you select the letter to the right of each letter. Similarly, if they are in the same column, then select the letter below each letter. If you are already at the last row or column position, you wrap to the first letter of that row or column.

For example, "SW" would be encoded as "UA". Of course, deciphering is the reverse. The Playfair cipher could be used with different key phrases for each user and the phrase could change daily.


This is a relatively strong pencil and paper cipher. The solution to this cipher was published in the first US government document on cryptology by Lieutenant Joseph O.

Mauborgne went on to become a Major General and Chief Signal Officer with several major accomplishments to his credit. He was the first person to demonstrate the use of a radio in an airplane; he reinvented the Jefferson wheel cypher into a 25 wheel cipher, the M; he designed the one-time pad and proved it is the only theoretically unbreakable cipher and he was the Chief Signal Officer when the Japanese Purple cipher was broken just prior to WW2.

At the end of WWI, a proliferation of rotor based cipher machines were independently invented by four men in four different countries within the space of a few years.

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These are all polyalphabetic ciphers with each rotor wired to have a different substitution alphabet. Several rotors were placed in series to give a complex algorithm where each letter of a message is substituted several times.

This type of machine provided a much stronger cipher but also simplified the operations for the users, both ciphering and deciphering was accomplished in similar fashion to using a typewriter.

Almost all were broken by the enemy. First rotor cipher machines Inventors: Apparently, he had time to think about cryptography and between to patented several cipher devices, including a check writing device, a cipher keyboard and two electric typewriters connected with 26 wires for automatic monoalphabetic ciphering.

Hebern built his first rotor cipher in This first cipher machine had only one rotor which could be taken out and reversed to use in decipher mode.

He even wrote an ode to his cipher machine: Friedman pointed out a major shortcoming of the Hebern design or the design of any rotor cipher with odometer style stepping, including the Enigma. With this design, only one rotor spins and the other rotors are fixed for 26 characters of a message, making it vulnerable to cryptanalysis.

Friedman went on to invent the SIGABA cipher machine, with its irregular stepping, which was one of the very few ciphers not broken by the enemy in WW2. Hebern went on to sell only a dozen machines before going bankrupt, ending up in jail again for defrauding his investors.

Arthur Scherbius A German engineer, Arthur Scherbius, was the second inventor of a rotor cipher, which he called the Enigma machine enigma has the same spelling and meaning in both German and English.Automorphisms of Sn and of An In this note we prove that if n 6= 6, then Aut(Sn)»= Sn»= Aut(An).

In particular, when The conjugacy class of the product of k disjoint transpositions is the If ¾ = ¿1 ¢¢¢¿k is a product of k ‚ 2 disjoint 3-cycles, write.

The representation of a permutation as a product of transpositions is not unique, but the parity of the number of transpositions in the product is a feature of the permutation and does not depend on the representation.

Any permutation can be represented as a product of cycles.

A blog about probability and olympiads by Dominic Yeo

The problem of construction and analysis of the properties of composition of several transpositions of a special class and analysis of the results of their influence on some permutation is important. Aug 14,  · Write the permutation P= in cycle notation, and then write it as a product of transpositions 2.

Relevant equations 3. The attempt at a solution I got the cycle notation to be ()(), but i am now not sure now to write it as a product of transpositions. The final product reflects the truth that I still have a very limited capacity for writing intricate harmony, though the piece is comparatively more complex than my previous settings of Donne’s work.

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