Thursday, November 11, 2010

Phi Test Results On D'Agapeyeff Cipher

The follow are results from phi tests I ran.  The first is with the original ciphertext, where each of the 392 numbers are paired after removing the final three zeros.


The observed score, Phi(o), in all three tests indicate the frequencies of the number pairs resemble English text.  This holds true when breaking the ciphertext into two 7x14 rectangles before and after the "04".




The second test I ran was on the ciphertext after removing the 6s, 7s, 8s, 9s, and all zeros. The remaining numbers (1-5) were then paired.


The observed phi value for the 98 number pairs was much closer to Phi(r) for random letters than for Phi(e) which is what would have been expected for English text.

Breaking the 98 pairs into two groups of 49, before and after the zero in the middle of the ciphertext yields a phi value of 80 for the first half and 136 for the second half.  While the first half appears to be random letters, the second half could certainly  be English text.



The next test I ran on the D'Agapeyeff ciphertext again relied on removing the nulls (6-0), however I instead paired the digits before and after the zero in the middle of the ciphertext..  Pairing the 1st number with the 99th, the 2nd with the 100th, etc.

Again, the phi test for all 98 number pair frequencies is much too low to be considered readable English text, however testing the first 49 pairs and second 49 pairs separately yields phi values that can be considered in line with English.

I did want to complete one other test to see what the results would be for a 49 character cipher similar in language to what D'Agapeyeff was writing in his book.  So I tested the phrase:

THEENEM
YISCOMI
NGFROMT
HENORTH
WESTFRI
DAYATFO
URPMHRT

"THE ENEMY IS COMING FROM THE NORTHWEST FRIDAY AT FOUR PM HRT"

The score was as follows:



The observed phi value was very similar to the observed values on the previous test.  I'm not using this as a proof for the other test, merely as a point of comparison for a short message.


In my next post I will include some of my observations from breaking the cipher into smaller rectangles/squares.



No comments:

Post a Comment