Vinegar on Caesar salad

Number Theory Level 4

The Vigenère cipher is a type of encryption method for alphabetic text that involves a series of Caesar shift ciphers .

To encrypt a plaintext message such as ILOVEBRILLIANT with the Vigenère cipher, we perform these steps:

Choose a key , which is a word consisting of only alphabetic characters, e.g. MATH .
Write it out repeatedly until it matches the length of the message to create a key message: MATHMATHMATHMA .
Encode each letter in the original message using a Caesar shift from A to the corresponding letter in the key message. For example, the first letter I of the original message becomes U in the encoded message, because we performed the Caesar shift A -> M on it. The second letter L is unchanged because A -> A does nothing.
Continue encoding each character until the entire message is encoded. In this example, the final encoded message is ULHCQBKPXLBHZT .

The following text has been encrypted with the Vigenère cipher. What is the length of the key? $($ Input $-1$ if you think the length of the key cannot be determined. $)$

uyqcemeavpstghsjibppvcutzkvvwcamhqgucfvxizzepmnpacfvxpatamhqguofd

Hint: This problem is not meant to be solved by programming!

The answer is 13.

1 solution

Giorgos K.
Mar 27, 2018

There is an easily seen repetition... uyqcemeavpstghsjibppvcutzkvvwcamhqgu cfvx izzepmnpa cfvx patamhqguofd

The distance between the repetitions of cfvx is 13

So, the length of the key could only be 13 or 1 and I went for 13 ;-)

EDIT : cracking the code

Firstly I subtracted the first 13 letters (concatenated 5 times) of the cipher text from the cipher text: In this way we get rid of the key but also we encrypt the cipher text using its 13 first letters as new key

$uyqcemeavpstghsjibppvcutzkvvwcamhqgucfvxizzepmnpacfvxpatamhqguofd$ $-$ $uyqcemeavpstguyqcemeavpstguyqcemeavpstguyqcemeavpstguyqcemeavpstg$ and got

$aaaaaaaaaaaaanutgxdlvhfbgebxgawadqlfkmpdkjxadinulkmpdrkrwadqlfwmx$

I knew that those were the 13 groups of 5 letters each but I needed to find the right shift for every group

then I thought to use "brilliant" as the first word and... bingo!

here is the secret message

$brilliantiscoolbrilliantiscoolhiddencodebrilliantcodeischiddenool$

and the original key (that we didn't use) is $thirteenchars$

Vinegar on Caesar salad

The answer is 13.

1 solution

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