Viewing Single Post From: Clarification

Viewing Single Post From: Clarification
aloos	Oct 28 2009, 02:12 PM
Just registered Posts: 2 Group: Members Member #3,291 Joined: October 12, 2009	Hello all, I find Osrics idea about how two disks are moved by some pattern of steps along with the position in text intriguing. Mathematically, one could say that the idea is the following: We have two (different?) permuations of the alphabet, realized by matrices P_1 and P_2, and a matrix S[ i ] shifting the alphabet cyclic by i steps. Moreover, we have one function f(i) : i -> i mod 26 and one function g(i): i -> something in 1...26, following some cycling pattern. The encryption is then done by the permutation corresponding to the matrix product S[ f(i) ] * P_2 * S[ g(i) ] * P_1 So, the final permutation depends only on the actual position i of the letter that has to be encrypted. As far as I know, this is somewhat similar to the Enigma-encryption. However, Osrics idea does not take into account something Deavours and Kruh are heavily emphasizing in their article: ``He [John Byrne Jr.] said that perfect accuracy was essential when enciphering a message because one error would distort the rest of the message.'' (Byrne, Deavours, Kruh, ``Chaocipher enters the coumputer age when its method is disclosed to cryptologia editors.'') ``And, an important shortcoming of the cipher -- make one error during encipherment and the message is garbled beyond repair -- is eliminated by its implementation on a computer.'' (Ibid.) Therefore, I think that the encryption depends not only on the position as Osric thought, but (also?) on preceding (cipher or plain) letters. The problem is: Simply replacing one of the functions f(i) or g(i) by a function depending on -- say -- the preceding cipher letter would mean that cycling would emerge pretty fast (as long as we don't assume to have a long instruction about how to move the other disk forward or backward, which would contradict to the fact that the system is easy). Nevertheless, I tested this idea assuming that the x_{i-1} (the preceding plaintext letter) or y_{i-1} (the preceding ciphertext letter) play a role when encoding letter x_i. No surprise: I could not find any cycle. Any ideas how we could modify the model? andreas


Clarification · Chaocipher