Читать книгу Cryptography, Information Theory, and Error-Correction - Aiden A. Bruen - Страница 49

We will now use the second principle of “coincidences,” to find the length of the keyword. The sequence of plain text letters in positions 1 to , to , , to , etc., should be approximately the same, especially if is large. It follows that a similar result holds true for the corresponding sequences of cipher text letters. Thus, if we slide the cipher text along itself and count the number of coincidences (i.e. agreements) at each displacement, then on average the maximum number of coincidences will occur after an integer multiple of the keyword length (i.e. the max occurs for some , ). This technique can be illustrated using the following example: We will first determine the period and use it to determine the nature of the keyword from a cipher text passage:

VVHZK	UHRGF	HGKDK	ITKDW	EFHEV	SGMPH
KIUWA	XGSQX	JQHRV	IUCCB	GACGF	SPGLH
GFHHD	MHZGF	BSPSW	SDSXR	DFHEM	OEPGI
QXKZW	LGHZI	PHLIV	VFIPH	XVA

To find , write the cipher text on a long strip of paper, and copy it onto a second strip of paper beneath the first strip. For a displacement of 1, move the bottom strip to the left by one letter and count the number of character coincidences. Repeat this process for several displacements until the maximum displacement is obtained. The shift shown below corresponds to a displacement of 3:

V

V

H

Z

K

U

H

R

G

F

H

G

K

D

V

V

H

Z

K

U

H

R

G

F

H

G

K

D

K

I

T

By repeating this process for a number of displacements, we obtain Table 2.2:

Table 2.2 Number of character coincidences corresponding to displacement

Displacement	Number of coincidences
1	4
2	4
3	9
4	12
5	5
6	2
7	7
8	7

From our results, the maximum number of occurrences appears for a displacement of 4. Since we know the maximum displacement occurs for a scalar multiple of the period, the period is likely either 2 or 4.