Implementering af Affine Cipher
Den Affine-chiffer er en type monoalfabetisk substitutionsciffer, hvor hvert bogstav i et alfabet er afbildet til dets numeriske ækvivalent krypteret ved hjælp af en simpel matematisk funktion og konverteret tilbage til et bogstav. Den anvendte formel betyder, at hvert bogstav krypterer til et andet bogstav og tilbage igen, hvilket betyder, at chifferen i det væsentlige er en standard substitutionsciffer med en regel, der styrer, hvilket bogstav der går til hvilket.
Hele processen er afhængig af at arbejde modulo m (længden af det anvendte alfabet). I den affine chiffer afbildes bogstaverne i et alfabet af størrelse m først til heltal i området 0 … m-1.
'Nøglen' til Affine-chifferet består af 2 numre, vi kalder dem a og b. Den følgende diskussion antager brugen af et alfabet på 26 tegn (m = 26). a bør vælges til at være relativt prime til m (dvs. a bør ikke have nogen faktorer til fælles med m).
Kryptering
Den bruger modulær aritmetik til at transformere det heltal, som hvert almindeligt bogstav svarer til, til et andet heltal, der svarer til et chiffertekstbogstav. Krypteringsfunktionen for et enkelt bogstav er
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.
Dekryptering
Ved dechifrering af chifferteksten skal vi udføre de modsatte (eller omvendte) funktioner på chifferteksten for at hente klarteksten. Endnu en gang er det første skridt at konvertere hvert af chiffertekstbogstaverne til deres heltalsværdier. Dekrypteringsfunktionen er
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 .
At finde en multiplikativ invers
Vi skal finde et tal x, således at:
Hvis vi finder tallet x sådan, at ligningen er sand, er x det inverse af a, og vi kalder det a^-1. Den nemmeste måde at løse denne ligning på er at søge i hvert af tallene 1 til 25 og se, hvilken der opfylder ligningen.
[gxd] = gcd(am); % we can ignore g and d we dont need them x = mod(xm);
Hvis du nu ganger x og a og reducerer resultatet (mod 26) får du svaret 1. Husk at dette kun er definitionen af en invers, dvs. hvis a*x = 1 (mod 26) så er x en invers af a (og a er en invers af x)
Eksempel:
Implementering:
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.
Produktion
Encrypted Message is : UBBAHK CAPJKX Decrypted Message is: AFFINE CIPHER
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