Decrypting Vigenere Cipher

[CleoZ]

I have a question from my coursework I am stuck on.

Two 10 letter words w1 and w2 were chosen from the list at https://www.bestwordlist.com/10letterwords.htm and encrypted using a keyword k a random string of 10 characters. Two ciphertexts are produced c1: NXPRKTZPM and c2:ZQTRRYVNPM. The same keyword k is used for both encryptions. Find the two plaintexts wi an w2 and the original key k.


I have tried to figure it out but got stuck. There must be an easier way than going through every single 10 letter word.

Please Help

The coursework is due in on Tuesday 17th

[scrunge999]

Hi Outzam,

It would help if we had some more background about the coursework that this question forms part of. Are you expected to decrypt the two encoded words manually or to write a program to do it? If you have to do this by hand I can’t think of an easy way of doing it. I have provided design notes for one possible solution above. I can’t see how posting the plaintext and keyword would help - I can’t imagine you would be awarded many marks for simply giving the answer without explaining how you arrived at it. And if I just tell you the answer you will have learned nothing.

Normally, solving a Vigenère (polyalphabetic) cipher by hand would require a longer encrypted message than 2 x 10 characters. You could then use frequency analysis and also look for recurring patterns in the ciphertext to determine the length of the keyword. The fact that you’ve been given two encrypted words and the length of the keyword would suggest that you are expected to solve this programmatically. My brute force approach looks for two words in the word list where each letter in the second word is the following number of letters further in the alphabet than the first word:
1: 12
2: 19
3: 4
4: 0
5: 7
6: 5
7: 11
8: 14
9: 0
10: 0

If you write some code that does this you will find the solution. There is only one pair of words in the word list that matches the above pattern.

[carterluke]

Here’s a step-by-step guide:

Understand the encryption method: If the encryption is based on a simple substitution or XOR operation, you can compare corresponding characters in c1c1c1 and c2c2c2 with their plaintext counterparts.

Use frequency analysis: The ciphertexts c1:NXPRKTZPMc1: NXPRKTZPMc1:NXPRKTZPM and c2:ZQTRRYVNPMc2: ZQTRRYVNPMc2:ZQTRRYVNPM give clues about the key. Start by checking how the same letters in w1w1w1 and w2w2w2 are transformed into ciphertext.

Cross-check the list: Use the 10-letter word list to find possible candidates for w1w1w1 and w2w2w2. You can reduce the possibilities by focusing on letters that align with the given ciphertext patterns.

Use tools: To save time, use a word-solving tool like https://wordslibrary.com/10-letter-word-finder/ to find matching words based on the encrypted patterns.

Example Process:

Suppose k[i]=c1[i]⊕w1quote[k] = c1quote[ \oplus w1[i]k]=c1[i]⊕w1[i] for each character iii, where ⊕\oplus⊕ is the XOR or substitution operation.

Once you deduce kkk, verify it with c2[i]=w2[i]⊕kquote[c2] = w2quote[ \oplus k[i]c2]=w2[i]⊕k[i] to confirm w2w2w2.