![playfair cipher playfair cipher](https://image.slidesharecdn.com/cryptography-170309030037/95/cryptography-27-638.jpg)
![playfair cipher playfair cipher](https://i.ytimg.com/vi/quKhvu2tPy8/maxresdefault.jpg)
You obviously don't know what the value of $k$ is, but there's nothing to stop you testing for key lengths corresponding to every divisor of $2kn$.Įven if your plaintext contains no repeated words whatsoever, you're still vulnerable to the same attack if the same word appears in more than one message. So you still haven't eliminated the primary weakness of vanilla Vigenère.įor example, if your Vigenère key has length $n$, just one repetition of a word at an interval of $2kn$ places provides enough information to get started on an attack. Specifically, although the combination of Playfair and Vigenère does reduce the frequency of repeated sequences, it doesn't get rid of them.
![playfair cipher playfair cipher](https://bermoskin.weebly.com/uploads/1/2/7/1/127126766/404978585.png)
Aiming for something "considerably more secure" than either of these is really setting the bar very low. It would be considerably more secure.īut nowadays, classical encryption methods like Playfair and Vigenère are so easily broken by computer analysis that they offer next to no security whatsoever. This means that the distances between the repetitions are significantly larger and could have significantly more factors, which would mean the length of the key is less certain to the cryptanalyst. If $E_1(P)$ produces n repeated sequences (a single repetition) of average distance m apart, $E_2(P)$ will, on average, produce 2 different repeated sequences, each with $n/2$ repetitions that are $2*n*$ distance apart. Four letter repetitions suffer a similar fate - half the time, the Playfair pass will instead make them into repeated sequences of length two as well. Repeated sequences aren't quite as clear - particularly shorter ones (which are the most common): sequences of length 3 (notably the word 'the') for example, become one of two sequences of length two, which is considerably easier to form by chance (which is why repeated sequences of length 2 are often not used in Vigenère cryptanalysis). In addition, any given sequence will become one of two entirely different sequences based on where the beginning of the sequence falls at the start of a Playfair pair or not. If E1 showed repetitions of odd length n, $E_2$ would show those same repetitions of length $n-1$ with either the final character or the first character missing, while even length repetitions would either be reproduced at length n or have both the end and the beginning cut off for length $n-2$. However, with an $E_2$ cipher on the same ciphertext, this won't work nearly as well. When trying to decrypt $E_1$, the first step is looking for repeated sequences of characters and recording their distance apart to help determine the length of the key, which is likely to be a factor of many of these recorded distances. When discussing $E_2$, assume all references to it's key will be referring to the key of it's Vigenère cipher unless explicitly stated otherwise.
![playfair cipher playfair cipher](https://image3.slideserve.com/6219235/adfgx-ciphers-l.jpg)
Would combining these two schemes give a considerably stronger encryption than either one individually?Ĭonsider two encryption schemes: one in which only the Vigenère cipher is used (which I'll call $E_1$), and one in which both the Vigenère and Playfair cipher is used ( $E_2$). I'm researching cryptography for a school project, came across the above two ciphers, and something occurred to me.