Vigenere decryption oddity

Question

I have written a java program that encodes with the Vigenere cipher the encryption works fine, however the decryption does not for some special cases.

For example if the plain text is 'k' and the key is 'y' it correctly produces the cipher text 'i' ((10 + 24 = 34 % 26 = 8))

however when decrypting the cipher text is 'i' and the key is 'y' I get((8-24) =-16%26 = -16)) which even if it was positive would be Q. When it should correctly decrypt back to 'k' which would be 10.

Can anyone help me out here? I can post more code if needed.

---Link to wiki Viginare cipher algorithm http://en.wikipedia.org/wiki/Vigen%C3%A8re_cipher ---

        //decryption
    else{
        for (int i=0; i < a.length(); i++){

                for (int j=0; j < full.length(); j++){
                    //finding the index of the current cipher text letter
                    if (a.charAt(i) == full.charAt(j)){
                        positionP = j;

                    }
                    //finding the index of the current key letter
                    if(key.charAt(i)==full.charAt(j)){
                        positionK = j;
                    }


                }
                //using the formula for vigenere encoding it adds the newly encrypted character to the output
                output = output + full.charAt((positionP - positionK)%26);
            }
        }

Answer 1

Note that the remainder operator in Java is defined such that the magnitude of the result is always less than the magnitude of the divisor, and the result of the remainder operation is negative if the dividend is negative [JLS].

You may obtain the desired output by doing:

 output = output + full.charAt((positionP - positionK + 26)%26);

If positionP-positionK is positive, the addition doesn't change the result (because 26%26=0). If positionP-positionK is negative (between -25 and 0), then positionP - positionK + 26 will be non-negative, yielding the correct result.

Answer 2

If your key is 'y'=24 and the length of your alphabet is 26 you have to shift alphabet-key= 26 - 24 = 2 to decrypt. You always have to add and then calculate mod 26.

So your code has to be

       //decryption
else{
    for (int i=0; i < a.length(); i++){

            for (int j=0; j < full.length(); j++){
                //finding the index of the current cipher text letter
                if (a.charAt(i) == full.charAt(j)){
                    positionP = j;

                }
                //finding the index of the current key letter
                if(key.charAt(i)==full.charAt(j)){
                    positionK = j;
                }


            }
            //using the formula for vigenere encoding it adds the newly encrypted character to the output
            output = output + full.charAt((positionP + (26-positionK))%26);
        }
    }