# Given an encryption key in a transposition cipher, find the decryption key

I am continuing my practice on problems for my cryptography class. I'm starting to get the hang of basic ideas of ciphers. At least i thought this until I attempted to do the follwng problem:

The encryption key in a transposition cipher is

$(5, 12, 3, 7, 9, 6, 4, 14, 1, 13, 10 , 8, 15, 2, 11,16)$.

Find the decryption key

I'm not even sure where or how to begin this problem. I've looked online to see if i came across any problems similar to this, but i have not found anything like this. Any help in pushing me in the right direction towards solving this would be greatly appreciated. Thanks!

Most of the stuff i've found involves words unlike this one.

• What kind of transposition cipher? That key suggests columnar transposition, but for that you wouldn't have a separate decryption key. – Brian M. Scott Jan 30 '15 at 23:14
• That is all the info I am given for this problem. – user655321 Jan 30 '15 at 23:23
• How would you go about starting to solve this problem? – user655321 Jan 31 '15 at 3:32
• I would need more information than is present in the actual problem statement. I can only guess that this information is implicit in the context of the material that you've been studying, to which I don't have access. – Brian M. Scott Jan 31 '15 at 3:47

Suppose your plaintext is 16 long: $p_1,p_2,\ldots,p_{16}$. Then the ciphertext, when we apply your key $(5,12,3,7,9,6,4,14,1,13,10,8,15,2,11,16)$ as a columnar transposition, equals $c_1 = p_9, c_2 = p_{14}, c_3 = p_3, c_4 = p_7, c_5 = p_1, c_6 = p_6, c_7 = p_4, c_8 = p_{12}, c_9 = p_{5}, c_{10} = p_{11}, c_{11} = p_{15}, c_{12} = p_2, c_{13} = p_{10}, c_{14} = p_8, c_{15} = p_{13}, c_{16} = p_{16}$.
So the key to go back from ciphertext to plaintext equals $(9,14,3,7,1,6,4,12,5,11,15,2,10,8,13,16)$