Cryptography - transposition cipher

[Rubik]

Suppose m = 6 was encoded with ther permutation \pi = (13)(2546)

Decrypt:- EESLSHSALSESLSHBLEHSYEETHRAEOS

It turns out that the inverse of \pi is how you decrypt the message and apply the inverse permutaion which is (31)(6452)

And the plaintext is she sells seashells...

However I am not sure how to work out the inverse function and then how to apply the inverse permutation to get that particular plain text any ideas?

 

[Stephen Tashi]

However I am not sure how to work out the inverse function

You mean how to work out the inverse permutation?
(6,4,5,2) sends 6 to 4, 4 to 5, etc. The inverse would undo that. It would send 4 to 6, 5 to 4 etc.

and then how to apply the inverse permutation to get that particular plain text any ideas?

(3,1) interchanges the first and 3rd letters, which changes EES to SES.

 

[Rubik]

You mean how to work out the inverse permutation?
(6,4,5,2) sends 6 to 4, 4 to 5, etc. The inverse would undo that. It would send 4 to 6, 5 to 4 etc.



(3,1) interchanges the first and 3rd letters, which changes EES to SES.

I am afraid I still do not understand? Why does EES become SES? And not SEE.

 

[Rubik]

And sorry what I meant before was how do you get the inverse permutation, so how does (13)(2546) become (31)(6452)?

 

[Rubik]

So basically I do not see how the inverse permutation makes the letters EESLSH goe to SHESEL?

 

[Stephen Tashi]

You are right (1,3) makes EES go to SEE, my mistake.

Let's do a simple example. Let the permutation be (1,3)(4,5,6)
This implies the mapping:
1->3
3->1
4->5
5->6
6->4

The inverse mapping reverses the process. It is:
3->1
1->3
5->4
6->5
4->6

You have to figure out how to write that mapping in the notation for permutations.
It would be (3,1) (5 4 6)

To get that you start with 3->1, then what does 1 go to? It goes back to 3, so you have finished one cyclic permutation. Then do 5->4. What does 4 go to? It goes to 6. What does 6 go to. It goes to 5, so you completed another cyclic permutation.

 

[Rubik]

Okay so if I have pi = (124)(36)(587) then

pi inverse = (214)(63)(587)?

 

[Rubik]

Okay so if I have pi = (124)(36)(587) then

pi inverse = (214)(63)(587)?

 

[Stephen Tashi]

The (587) in your inverse isn't right. You need to send 8 to 5 and send 7 to 8 and so forth.

 

[Rubik]

Also going back to the previous example with the pi inverse = (31)(6452)

I do not understand how EESLSH goes to SHESEL

See using that invers key means 3 goes to 1 so EES become SEE, 6 goes to 4 means SEELSH goes to SEEHSL and 5 goes to 2 means SEEHSL goes to SSEHEL.. I have no idea what I am doing wrong?

 

[Rubik]

Sorry of course so (587) becomes (857)?

 

[Rubik]

Oh wait I get it now so goes to 1 means SEELSH and 6 goes to 4 means SEEHSL 4 goes to 5 means SEESHL and 5 goes to 2 means SHESEL.

Thank you so much for all your help! :D