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A Gronsfeld substitution cipher is not constant The key speci es the number of steps taken through the alphabet to obtain the cipher character The number of steps can vary from zero to the number of characters which comprise the plain-text alphabet The key can be produced by random permutation generator Figure 12-9 provides an example of such a Gronsfeld cipher for an alphabet of 27 characters The number of alternative encodings is now N 2 for an N -character alphabet, with very few choices that are unadvisable A key containing many zeros would not provide satisfactory enciphering
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Instead of using random key numbers, another message can be used The ordinal values of the characters of the key message provide the amount of displacement in the alphabet value This technique is called the Vignere cipher The key text, of course, can be of any length, even as long as the message to be enciphered Blanks in the key may be ignored For instance, the key string "AMERICA OF THEE I SING" will generate a sequence K = 01 13 05 18 09 01 15 06 20 08 05 05 09 17 09 14 07 A Vignere procedure for a larger alphabet is shown in Example 12-2 Ordinal numbers representing the characters are added modulo the size of the alphabet, to determine the ordinal number of the cipher character
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Example 12-2
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/* Input is the linein, key, and option = true for enciphering, false for deciphering The result is in lineout */ cipher: PROCEDURE(linein,key,option,lineout) EXTERNAL; DECLARE (linein,lineout,key) CHAR; l line = LENGTH(linein); l key = LENGTH(key); lineout = ''; /* the typewriter alphabet */ DECLARE abc CHAR(89) INITIAL('0123456789AaBbCcDdEeFf /* Use one character to de ne the beginning of the key */ k = INDEX(SUBSTR(key,l key,1),abc); l key = l key-1; DO i = 1 TO l line; ord = INDEX (SUBSTR(linein,i,1),abc); kod = INDEX (SUBSTR(key,k,1),abc); IF option THEN kod = -kod; cord = MOD(ord+kod,89)+1; SUBSTR(lineout,i,1) = SUBSTR(abc,cord,1) k = MOD(k,l key)+1; END; RETURN; END cipher;
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An alternative to the addition of ordinal numbers, modulo the size of the alphabet, to determine the ordinal number of the cipher character can be used when the characters use a xed-bit space The exclusive-OR operation, used in Sec 3-5 for hashing, provides an operation which is symmetric for both enciphering and deciphering, as shown in Fig 12-10
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More sophisticated methods can be developed based on the two transformations discussed, but we rst will describe common procedures of decrypting so that we can evaluate the weaknesses of the basic enciphering techniques 12-7-2 Decryption The ease with which a message can be decrypted depends on a number of factors: Is the method known Is the source language known How many alternative encipherings did exist How much enciphered text using the same key is available Is any matching plain text available
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A basic tool to aid in the decrypting of a cipher text is the generation of a tableau If the method is known and the number of keys is limited, a tableau can be simply a listing of all possible decipherments The tableau is scanned by eye and the plain text message will probably stand out If many, but yet a reasonably nite number of decipherments are possible, a heuristic selection of deciphered text can reduce the volume of the tableau to be listed Simple heuristic algorithms might be that a vowel should exist in nearly all words, and that capitals and punctuation appear with certain regularity Tableaus which do not show unreasonable pattern are not presented If the source language is known, substitution ciphers can be attacked using known statistics of letter frequencies A simple substitution will generally yield the
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Sec 12-7
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