Cryptography, Information Theory, and Error-Correction. Aiden A. Bruen
Чтение книги онлайн.

Читать онлайн книгу Cryptography, Information Theory, and Error-Correction - Aiden A. Bruen страница 30

Название: Cryptography, Information Theory, and Error-Correction

Автор: Aiden A. Bruen

Издательство: John Wiley & Sons Limited

Жанр: Зарубежная компьютерная литература

Серия:

isbn: 9781119582403

isbn:

СКАЧАТЬ 1 right-parenthesis left-parenthesis 22 20 23 18 right-parenthesis EndLayout"/>

      The initial settings are defined with r 1 equals 22 (i.e. the letter at the top of roter 1 is upper V), r 2 equals 7, r 3 equals 12.

       For the signal traveling toward the reflector plate, the substitutions through the rotors are represented mathematically as follows:

StartLayout 1st Row 1st Column b 2nd Column equals 3rd Column upper R e m left-bracket a plus r 1 comma 26 right-bracket Superscript alpha 1 2nd Row 1st Column c 2nd Column equals 3rd Column upper R e m left-bracket b plus r 2 comma 26 right-bracket Superscript alpha 2 3rd Row 1st Column d 2nd Column equals 3rd Column upper R e m left-bracket c plus r 3 comma 26 right-bracket Superscript alpha 3 EndLayout

      where raising a term to the exponent alpha 1 means locating the term in the permutation set and replacing it with the number to the right of the term. If there is a bracket adjacent to the term, wrap around to the beginning of the subset. For example, with our settings as above, 3 Superscript alpha 1 Baseline equals 4 and 8 Superscript alpha 2 Baseline equals 0.

       Since the reflector has contacts which are only connected in pairs, we get

e equals left-parenthesis d right-parenthesis Superscript beta

      Once e has been output from the reflector, we follow the signal back to the keyboard:

StartLayout 1st Row c prime equals upper R e m left-bracket e Superscript alpha 3 Super Superscript negative 1 Superscript Baseline minus r 3 comma 26 right-bracket 2nd Row b prime equals upper R e m left-bracket c Superscript prime alpha 2 Super Superscript negative 1 Superscript Baseline minus r 2 comma 26 right-bracket 3rd Row a prime equals upper R e m left-bracket b Superscript prime alpha 1 Super Superscript negative 1 Superscript Baseline minus r 1 comma 26 right-bracket EndLayout

      r 1 is redefined as upper R e m left-bracket r 1 plus 1 comma 26 right-bracket. If r 1 equals 25 and we add 1, the new r 1 becomes 0 and r 2 is advanced by one.

      Similarly, if r 2 equals 25 and we add 1, the new r 2 becomes 0 and r 3 is advanced by one.

       Let us see what happens when we encode the letter “k,” which has numerical value 10.

StartLayout 1st Row 1st Column a 2nd Column equals 3rd Column 10 2nd Row 1st Column b 2nd Column equals 3rd Column upper R e m left-bracket a plus r 1 comma 26 right-bracket Superscript alpha 1 4th Column equals 5th Column upper R e m left-bracket 10 plus 22 comma 26 right-bracket Superscript alpha 1 6th Column equals 7th Column 6 Superscript alpha 1 8th Column equals 9th Column 10 3rd Row 1st Column c 2nd Column equals 3rd Column upper R e m left-bracket b plus r 2 comma 26 right-bracket Superscript alpha 2 4th Column equals 5th Column upper R e m left-bracket 10 plus 7 comma 26 right-bracket Superscript alpha 2 6th Column equals 7th Column 1 7 Superscript alpha 2 8th Column equals 9th Column 19 4th Row 1st Column d 2nd Column equals 3rd Column upper R e m left-bracket c plus r 3 comma 26 right-bracket Superscript alpha 3 4th Column equals 5th Column upper R e m left-bracket 19 plus 12 comma 26 right-bracket Superscript alpha 3 6th Column equals 7th Column 5 Superscript alpha 3 8th Column equals 9th Column 0 EndLayout

      Reaching the reflector, we get e equals left-parenthesis d right-parenthesis Superscript beta Baseline equals 0 Superscript beta Baseline equals 4. Now following the signal back through the rotors, we obtain

StartLayout 1st Row 1st Column c prime 2nd Column equals 3rd Column upper R e m left-bracket e Superscript alpha 3 Super Superscript negative 1 Superscript Baseline minus r 3 comma 26 right-bracket 4th Column equals 5th Column upper R e m left-bracket 4 Superscript alpha 3 Super Superscript negative 1 Superscript Baseline minus 12 comma 26 right-bracket 6th Column equals 7th Column upper R e m left-bracket 18 minus 12 comma 26 right-bracket 8th Column equals 9th Column 16 2nd Row 1st Column b prime 2nd Column equals 3rd Column upper R e m left-bracket c Superscript prime alpha 2 Super Superscript negative 1 Superscript Baseline minus r 2 comma 26 right-bracket 4th Column equals 5th Column upper R e m left-bracket 1 6 Superscript alpha 2 Super Superscript negative 1 Superscript Baseline minus 7 comma 26 right-bracket 6th Column equals 7th Column upper R e m left-bracket 15 minus 7 comma 26 right-bracket 8th Column equals 9th Column 8 3rd Row 1st Column a prime 2nd Column equals 3rd Column upper R e m left-bracket b Superscript prime alpha 1 Super Superscript negative 1 Superscript Baseline minus r 1 comma 26 right-bracket 4th Column equals 5th Column upper R e m left-bracket 8 Superscript alpha 1 Super Superscript negative 1 Superscript Baseline minus 22 comma 26 right-bracket 6th Column equals 7th Column upper R e m left-bracket 14 minus 7 comma 26 right-bracket 8th Column equals 9th Column 7 EndLayout

       Therefore, the first cipher text character corresponds to 7, and is thus is “H.”

      Now, we must update the rotor settings: r 1 equals 23 comma r 2 equals 7 comma r 3 equals 12.

      If the settings were such that r 1 was 25, the updating process would proceed as follows: r 1 equals 0, r 2 equals 8, r 3 equals 12.

       As mentioned above, an interesting aspect about the Enigma enciphering scheme is the fact that deciphering a message follows the exact same process.

СКАЧАТЬ