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