Chi test

The chi test (not to be confused with the chi-square test ) is a statistical test that is used especially in cryptanalysis to compare two texts. It was proposed by the American cryptanalyst Solomon Kullback in 1935 .

definition

The basis of the Chi test is the sum Chi , also referred to by Kullback as the "cross-product sum" , which is derived from the frequency of occurrences of individual characters m´ _i and m " _i in two texts T´ and T" of the same length M as is calculated as follows:

${\displaystyle Chi(T',T'')={\frac {1}{M^{2}}}\sum _{i=1}^{N}(m'_{i}\cdot m''_{i})}$

This definition is similar to the cross-correlation function known from signal analysis for describing the correlation of two signals.

application

Since the calculation of Chi in addition to counting the frequency of single characters ( letter frequencies ) m _{i of} the two texts and additions also requires multiplications and even a division when calculating the sum , the Chi test came because of the little developed in the 1930s Computer technology initially not for practical use. This changed in the 1940s with the advent of powerful electromechanical calculating machines and the first electronic calculators, the forerunners of today's computers . From 1944, the Chi test was carried out using the American RAM machines (abbreviation for "Rapid Analytical Machines" , German: "Fast analytical machines").

literature

• Friedrich L. Bauer : Deciphered Secrets. Methods and maxims of cryptology. 3rd, revised and expanded edition. Springer, Berlin et al. 2000, ISBN 3-540-67931-6 .

Individual evidence

1. ↑ ^{a b} Friedrich L. Bauer: Deciphered secrets. Methods and maxims of cryptology. 3rd, revised and expanded edition. Springer, Berlin et al. 2000, p. 342.
2. ↑ Friedrich L. Bauer: Deciphered secrets. Methods and maxims of cryptology. 3rd, revised and expanded edition. Springer, Berlin et al. 2000, p. 32 6ff.