Affine Cipherin käyttöönotto
Affine-salaus on eräänlainen yksiaakkosinen korvaussalaus, jossa jokainen aakkosten kirjain kartoitetaan numeeriseen vastineensa, joka on salattu yksinkertaisella matemaattisella funktiolla ja muunnetaan takaisin kirjaimeksi. Käytetty kaava tarkoittaa, että jokainen kirjain salataan yhdeksi kirjaimeksi ja takaisin, mikä tarkoittaa, että salaus on pohjimmiltaan tavallinen korvaava salaus, jonka sääntö määrää, mikä kirjain menee mihinkin.
Koko prosessi perustuu työskentelymoduuliin m (käytetyn aakkoston pituus). Affinisessa salauksessa m-koon aakkosten kirjaimet kartoitetaan ensin kokonaislukuihin välillä 0 … m-1.
Affine-salauksen "avain" koostuu kahdesta numerosta, joita kutsutaan nimellä a ja b. Seuraavassa keskustelussa oletetaan 26 merkin aakkosten käyttöä (m = 26). a tulee valita suhteellisen ensiluokkaiseksi m:lle (eli a:lla ei pitäisi olla yhteisiä tekijöitä m:n kanssa).
Salaus
Se käyttää modulaarista aritmetiikkaa muuntaakseen kokonaisluvun, jota jokainen selväkielinen kirjain vastaa, toiseksi kokonaisluvuksi, joka vastaa salakirjoituksen kirjainta. Yhden kirjaimen salaustoiminto on
E ( x ) = ( a x + b ) mod m modulus m: size of the alphabet a and b: key of the cipher. a must be chosen such that a and m are coprime.
Salauksen purku
Salatekstiä purettaessa meidän on suoritettava salatekstille päinvastaiset (tai käänteiset) toiminnot selkeän tekstin hakemiseksi. Jälleen kerran ensimmäinen askel on muuntaa kukin salatekstin kirjain niiden kokonaislukuarvoiksi. Salauksen purkutoiminto on
D ( x ) = a^-1 ( x - b ) mod m a^-1 : modular multiplicative inverse of a modulo m. i.e. it satisfies the equation 1 = a a^-1 mod m .
Kertovan käänteisen löytäminen
Meidän on löydettävä luku x, joka:
Jos löydämme luvun x sellaisena, että yhtälö on tosi, niin x on a:n käänteis ja kutsumme sitä a^-1:ksi. Helpoin tapa ratkaista tämä yhtälö on etsiä jokaista numeroa 1 - 25 ja katsoa, mikä täyttää yhtälön.
[gxd] = gcd(am); % we can ignore g and d we dont need them x = mod(xm);
Jos nyt kerrot x:n ja a:n ja pienennät tulosta (mod 26), saat vastauksen 1. Muista, että tämä on vain käänteisen määritelmä, eli jos a*x = 1 (mod 26), niin x on a:n käänteis (ja a on x:n käänteis).
Esimerkki:
Toteutus:
C++ //CPP program to illustrate Affine Cipher #include using namespace std ; //Key values of a and b const int a = 17 ; const int b = 20 ; string encryptMessage ( string msg ) { ///Cipher Text initially empty string cipher = '' ; for ( int i = 0 ; i < msg . length (); i ++ ) { // Avoid space to be encrypted if ( msg [ i ] != ' ' ) /* applying encryption formula ( a x + b ) mod m {here x is msg[i] and m is 26} and added 'A' to bring it in range of ascii alphabet[ 65-90 | A-Z ] */ cipher = cipher + ( char ) (((( a * ( msg [ i ] - 'A' ) ) + b ) % 26 ) + 'A' ); else //else simply append space character cipher += msg [ i ]; } return cipher ; } string decryptCipher ( string cipher ) { string msg = '' ; int a_inv = 0 ; int flag = 0 ; //Find a^-1 (the multiplicative inverse of a //in the group of integers modulo m.) for ( int i = 0 ; i < 26 ; i ++ ) { flag = ( a * i ) % 26 ; //Check if (a*i)%26 == 1 //then i will be the multiplicative inverse of a if ( flag == 1 ) { a_inv = i ; } } for ( int i = 0 ; i < cipher . length (); i ++ ) { if ( cipher [ i ] != ' ' ) /*Applying decryption formula a^-1 ( x - b ) mod m {here x is cipher[i] and m is 26} and added 'A' to bring it in range of ASCII alphabet[ 65-90 | A-Z ] */ msg = msg + ( char ) ((( a_inv * (( cipher [ i ] + 'A' - b )) % 26 )) + 'A' ); else //else simply append space character msg += cipher [ i ]; } return msg ; } //Driver Program int main ( void ) { string msg = 'AFFINE CIPHER' ; //Calling encryption function string cipherText = encryptMessage ( msg ); cout < < 'Encrypted Message is : ' < < cipherText < < endl ; //Calling Decryption function cout < < 'Decrypted Message is: ' < < decryptCipher ( cipherText ); return 0 ; }
Java // Java program to illustrate Affine Cipher class GFG { // Key values of a and b static int a = 17 ; static int b = 20 ; static String encryptMessage ( char [] msg ) { /// Cipher Text initially empty String cipher = '' ; for ( int i = 0 ; i < msg . length ; i ++ ) { // Avoid space to be encrypted /* applying encryption formula ( a x + b ) mod m {here x is msg[i] and m is 26} and added 'A' to bring it in range of ascii alphabet[ 65-90 | A-Z ] */ if ( msg [ i ] != ' ' ) { cipher = cipher + ( char ) (((( a * ( msg [ i ] - 'A' )) + b ) % 26 ) + 'A' ); } else // else simply append space character { cipher += msg [ i ] ; } } return cipher ; } static String decryptCipher ( String cipher ) { String msg = '' ; int a_inv = 0 ; int flag = 0 ; //Find a^-1 (the multiplicative inverse of a //in the group of integers modulo m.) for ( int i = 0 ; i < 26 ; i ++ ) { flag = ( a * i ) % 26 ; // Check if (a*i)%26 == 1 // then i will be the multiplicative inverse of a if ( flag == 1 ) { a_inv = i ; } } for ( int i = 0 ; i < cipher . length (); i ++ ) { /*Applying decryption formula a^-1 ( x - b ) mod m {here x is cipher[i] and m is 26} and added 'A' to bring it in range of ASCII alphabet[ 65-90 | A-Z ] */ if ( cipher . charAt ( i ) != ' ' ) { msg = msg + ( char ) ((( a_inv * (( cipher . charAt ( i ) + 'A' - b )) % 26 )) + 'A' ); } else //else simply append space character { msg += cipher . charAt ( i ); } } return msg ; } // Driver code public static void main ( String [] args ) { String msg = 'AFFINE CIPHER' ; // Calling encryption function String cipherText = encryptMessage ( msg . toCharArray ()); System . out . println ( 'Encrypted Message is : ' + cipherText ); // Calling Decryption function System . out . println ( 'Decrypted Message is: ' + decryptCipher ( cipherText )); } } // This code contributed by Rajput-Ji
Python # Implementation of Affine Cipher in Python # Extended Euclidean Algorithm for finding modular inverse # eg: modinv(7 26) = 15 def egcd ( a b ): x y u v = 0 1 1 0 while a != 0 : q r = b // a b % a m n = x - u * q y - v * q b a x y u v = a r u v m n gcd = b return gcd x y def modinv ( a m ): gcd x y = egcd ( a m ) if gcd != 1 : return None # modular inverse does not exist else : return x % m # affine cipher encryption function # returns the cipher text def affine_encrypt ( text key ): ''' C = (a*P + b) % 26 ''' return '' . join ([ chr ((( key [ 0 ] * ( ord ( t ) - ord ( 'A' )) + key [ 1 ] ) % 26 ) + ord ( 'A' )) for t in text . upper () . replace ( ' ' '' ) ]) # affine cipher decryption function # returns original text def affine_decrypt ( cipher key ): ''' P = (a^-1 * (C - b)) % 26 ''' return '' . join ([ chr ((( modinv ( key [ 0 ] 26 ) * ( ord ( c ) - ord ( 'A' ) - key [ 1 ])) % 26 ) + ord ( 'A' )) for c in cipher ]) # Driver Code to test the above functions def main (): # declaring text and key text = 'AFFINE CIPHER' key = [ 17 20 ] # calling encryption function affine_encrypted_text = affine_encrypt ( text key ) print ( 'Encrypted Text: {} ' . format ( affine_encrypted_text )) # calling decryption function print ( 'Decrypted Text: {} ' . format ( affine_decrypt ( affine_encrypted_text key ) )) if __name__ == '__main__' : main () # This code is contributed by # Bhushan Borole
C# // C# program to illustrate Affine Cipher using System ; class GFG { // Key values of a and b static int a = 17 ; static int b = 20 ; static String encryptMessage ( char [] msg ) { /// Cipher Text initially empty String cipher = '' ; for ( int i = 0 ; i < msg . Length ; i ++ ) { // Avoid space to be encrypted /* applying encryption formula ( a x + b ) mod m {here x is msg[i] and m is 26} and added 'A' to bring it in range of ascii alphabet[ 65-90 | A-Z ] */ if ( msg [ i ] != ' ' ) { cipher = cipher + ( char ) (((( a * ( msg [ i ] - 'A' )) + b ) % 26 ) + 'A' ); } else // else simply append space character { cipher += msg [ i ]; } } return cipher ; } static String decryptCipher ( String cipher ) { String msg = '' ; int a_inv = 0 ; int flag = 0 ; //Find a^-1 (the multiplicative inverse of a //in the group of integers modulo m.) for ( int i = 0 ; i < 26 ; i ++ ) { flag = ( a * i ) % 26 ; // Check if (a*i)%26 == 1 // then i will be the multiplicative inverse of a if ( flag == 1 ) { a_inv = i ; } } for ( int i = 0 ; i < cipher . Length ; i ++ ) { /*Applying decryption formula a^-1 ( x - b ) mod m {here x is cipher[i] and m is 26} and added 'A' to bring it in range of ASCII alphabet[ 65-90 | A-Z ] */ if ( cipher [ i ] != ' ' ) { msg = msg + ( char ) ((( a_inv * (( cipher [ i ] + 'A' - b )) % 26 )) + 'A' ); } else //else simply append space character { msg += cipher [ i ]; } } return msg ; } // Driver code public static void Main ( String [] args ) { String msg = 'AFFINE CIPHER' ; // Calling encryption function String cipherText = encryptMessage ( msg . ToCharArray ()); Console . WriteLine ( 'Encrypted Message is : ' + cipherText ); // Calling Decryption function Console . WriteLine ( 'Decrypted Message is: ' + decryptCipher ( cipherText )); } } /* This code contributed by PrinciRaj1992 */
JavaScript //Javascript program to illustrate Affine Cipher //Key values of a and b let a = 17 ; let b = 20 ; function encryptMessage ( msg ) { ///Cipher Text initially empty let cipher = '' ; for ( let i = 0 ; i < msg . length ; i ++ ) { // Avoid space to be encrypted if ( msg [ i ] != ' ' ) /* applying encryption formula ( a x + b ) mod m {here x is msg[i] and m is 26} and added 'A' to bring it in range of ascii alphabet[ 65-90 | A-Z ] */ cipher = cipher + String . fromCharCode (((( a * ( msg [ i ]. charCodeAt ( 0 ) - 65 ) ) + b ) % 26 ) + 65 ); else //else simply append space character cipher += msg [ i ]; } return cipher ; } function decryptCipher ( cipher ) { let msg = '' ; let a_inv = 0 ; let flag = 0 ; //Find a^-1 (the multiplicative inverse of a //in the group of integers modulo m.) for ( let i = 0 ; i < 26 ; i ++ ) { flag = ( a * i ) % 26 ; //Check if (a*i)%26 == 1 //then i will be the multiplicative inverse of a if ( flag == 1 ) { a_inv = i ; } } for ( let i = 0 ; i < cipher . length ; i ++ ) { if ( cipher [ i ] != ' ' ) /*Applying decryption formula a^-1 ( x - b ) mod m {here x is cipher[i] and m is 26} and added 'A' to bring it in range of ASCII alphabet[ 65-90 | A-Z ] */ msg = msg + String . fromCharCode ((( a_inv * (( cipher [ i ]. charCodeAt ( 0 ) + 65 - b )) % 26 )) + 65 ); else //else simply append space character msg += cipher [ i ]; } return msg ; } //Driver Program let msg = 'AFFINE CIPHER' ; //Calling encryption function let cipherText = encryptMessage ( msg ); console . log ( 'Encrypted Message is : ' + cipherText ); //Calling Decryption function console . log ( 'Decrypted Message is: ' + decryptCipher ( cipherText )); // The code is contributed by Arushi Jindal.
Lähtö
Encrypted Message is : UBBAHK CAPJKX Decrypted Message is: AFFINE CIPHER
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