Bases of cryptographic protection of the information
The work purpose
Research of the basic methods cryptographic information are sewn up
Instructions to work
The cryptography - provides concealment of sense of the message by means of enciphering and its opening ðàñøèôðîâàíèåì which are carried out on special algorithms by means of keys.
Key - a concrete confidential status of some parametres of algorithm of the cryptographic data transformation, providing a choice only one variant from all possible for the given algorithm.
Cryptoanalyses - is engaged in opening of the code number without knowledge of a key (check of stability of the code number).
Coding - (does not concern cryptography) - system of the schematic symbols applied at information transfer. It is applied to increase in quality of information transfer, compression of the information and for reduction of cost of storage and transfer.
Cryptographic transformations have the purpose to provide inaccessibility of the information to the persons who do not have a key, and maintenance with demanded reliability of detection of unapproved distortions.
The majority of protection frames of the information is based on use of cryptographic code numbers and enciphering-rasshifrovanija procedures. According to the standard of GOST 28147-89 as the code number understand set of reversible transformations of set of the open data on set of the ciphered data set by a key and algorithm of transformation.
In cryptography following basic algorithms of enciphering are used:
· Algorithm of replacement (substitution) - symbols of the ciphered text are replaced with symbols of same or other alphabet according to in advance caused scheme of replacement;
· Algorithm of shift - symbols of the ciphered text are rearranged by a certain rule within some block of this text;
· ãàììèðîâàíèå - symbols of the ciphered text develop with symbols of some casual sequence;
· Analytical transformation - transformation of the ciphered text by some analytical rule (formula).
Processes of enciphering and ðàñøèôðîâàíèÿ are carried out within the limits of some êðèïòîñèñòåìû. For symmetric êðèïòîñèñòåìû application of the same key is characteristic both at enciphering, and at ðàñøèôðîâàíèè messages. In asymmetric êðèïòîñèñòåìàõ for çàøèôðîâàíèÿ the data one (popular) key, and for ðàñøèôðîâàíèÿ - other (confidential) key is used.
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Symmetric êðèïòîñèñòåìû
Shift code numbers
In code numbers of the Middle Ages tables with which help the simple procedures of enciphering based on shift of letters in the message were carried out were often used. Êëþ÷åì in this case is the sizes of the table. For example, the message “Not clear becomes not clearer” registers in the table of 5 lines and 7 columns on columns.
| Н | О | Н | С | Б | Н | Я |
| Е | Е | О | Я | О | Е | Т |
| Я | С | В | Е | Л | П | Н |
| С | Т | И | Щ | Е | О | Ы |
| Н | А | Т | Е | Е | Н | М |
For reception øèôðîâàííîãî messages the text is read out in the lines and grouped on 5 letters:
NONSB NJAEEO JAOETJA SVELP NSTISHCH EOYNA ÒÅÅÍÌ
A little áîëüøåé firmness to disclosing the method of single shift on a key possesses. It differs from previous that table columns are rearranged on a keyword, a phrase or a set of numbers of a line of the table. Using as a key a word the ЛУНАТИК, we will receive the following table
| Л | У | Н | А | Т | И | К | А | И | К | Л | Н | Т | У | ||
| Н | О | Н | С | Б | Н | Я | С | Н | Я | Н | Н | Б | О | ||
| Е | Е | О | Я | О | Е | Т | Я | Е | Т | Е | О | О | Е | ||
| Я | С | В | Е | Л | П | Н | Е | П | Н | Я | В | Л | С | ||
| С | Т | И | Щ | Е | О | Ы | Щ | О | Ы | С | И | Е | Т | ||
| Н | А | Т | Е | Е | Н | М | Е | Н | М | Н | Т | Е | А |
Before shift After shift
In top line of the left table the key is written down, and numbers under key letters are defined according to natural order of corresponding letters of a key in the alphabet. If in a key there would be identical letters, they would be numbered from left to right. The encryption turns out: SNJANN BOJAET EOOEE PNJAVL SSHCHOYS IETEN ÌÍÒÅÀ. For maintenance of additional reserve it is possible to cipher the message which has already been ciphered repeatedly. For this purpose the size of the second table select so that lengths of its lines and columns differed from lengths of lines and columns of the first table. Is better, if they are mutually simple.
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Except algorithms of single shifts algorithms of double shifts are applied. At first in the table the message text registers, and columns, and then then are serially rearranged lines. At decoding the order of shifts was return. The example of the given method of enciphering is shown in following tables:
| П | Р | И | Е | И | П | Е | Р | А | З | Ю | Ж | |||||
| З | Ж | А | Ю | А | Ю | Ж | Е | _ | С | Ш | ||||||
| _ | Ш | Е | С | Е. | _ | С | Ш | Г | Т | О | О | |||||
| Т | О | Г | О | Г | Т | О | О | И | П | Е | Р |
Double shift of columns and lines
As a result of shift encryption ÀÇÞÆÅ_ÑØÃÒÎÎÈÏÅÐ is received. As a key to the code number numbers of columns 2413 and row numbers 4123 of the initial table serve.
The number of variants of double shift quickly enough increases with increase in the size of the table: for table 3 õ 3 them 36, for 4 õ 4 them 576, and for 5*5 them 14400.
In the Middle Ages magic squares were applied to enciphering also. As magic squares are called square tables with the consecutive natural numbers entered in their cages, since unit which give in the sum on each column, each line and each diagonal the same number. For enciphering it is necessary to enter the initial text on the numbering resulted in a square and then to copy table contents in the lines. As a result it turns out øèôðîòåêñò, generated thanks to shift of letters of the initial message.
| О | И | Р | Т | ||||||
| З | Ш | Е | Ю | ||||||
| _ | Ж | А | С | ||||||
| Е | Г | О | П |
| П | Р | И | Е | З | Ж | А | Ю | _ | Ш | Е | С | Т | О | Г | О |
number of magic squares very sharply increases with increase in the size of its parties: for table 3*3 of such squares-1; for table 4*4 - 880; and for table 5*5-250000.
Code numbers of simple replacement
System of enciphering of Caesar - a special case of the code number of simple replacement. The method is based on replacement of each letter of the message by other letter of the same alphabet, by displacement from an initial letter on K letters.
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Known phrase Julia Caesar VENI VINI VICI - has come, has seen, has won, ciphered by means of the given method, it will be transformed in SBKF SFAF SFZF (at displacement on 4 symbols).
By the Greek writer Polibiem for 100 years BC has been invented so-called ïîëèáèàíñêèé the square in the size 5*5 filled with the alphabet in a casual order. The Greek alphabet has 24 letters, and 25th symbol is the blank. For enciphering on a square found a letter of the text and wrote down in øèôðîòåêñò a letter located below it in the same column. If the letter appeared in table bottom line took the top letter from this a column.